How to find the circumference and area of a circle

This article was co-authored by Grace Imson, MA. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University.

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Finding the area of a circle is a straightforward calculation if you know the length of the circle’s radius. If you don’t know the radius, however, you can still calculate the area if you are given the length of the circle’s circumference or perimeter. You can use a two-step process, solving first for the radius using the formula for the circumference: circumference = 2 π ( r ) <\displaystyle <\text>=2\pi (r)> . Then you can use the formula area = π ( r 2 ) <\displaystyle <\text >=\pi (r^<2>)> to find the area. You can also use the formula circumference = 2 π ( A ) <\displaystyle <\text>=2<\sqrt <\pi (A)>>> , which expresses the circumference of a circle as a function of its area, without knowing the length of the radius at all.

A circle is the set of all points in the plane that are a fixed distance from a fixed point also known as the center.

While area of circle is the space occupied by the circle in a two-dimensional plane circumference is the distance around a circle.

Formula to calculate area of a circle from perimeter.

Since we know the formula to calculate the circumference, this makes it easy to find the radius of the circle and in turn find its area.

How to find the circumference and area of a circle

π stands for pi

r is the radius of the circle.

When we make radius the subject we get;

Once you have the radius you use the formula below to find area of the circle.

Example:

Calculate the area of a circle whose circumference is 154 cm.

How to find the circumference and area of a circle

Therefore, the radius is 24.5 cm.

We proceed to find the area of the circle.

How to find the circumference and area of a circle

Therefore, the area of the circle is 1886.5 cm².

How to find the circumference and area of a circle

Area, Circumference & Diameter of Circle – work with steps

Input Data :
Radius = 8 in

Objective :
Find the area of circle.

Solution :
Area = πr 2
= 3.14 x (8) 2
= 3.14 x (64)
Area = 201.1429 in²

Area and circumference of circle calculator uses radius length of a circle, and calculates the perimeter and area of the circle. It is an online Geometry tool requires radius length of a circle. Using this calculator, we will understand methods of how to find the perimeter and area of a circle.
It is necessary to follow the next steps:

  1. Enter the radius length of a circle in the box. The value must be positive real number or parameter. Note that the length of a segment is always positive;
  2. Press the “GENERATE WORK” button to make the computation;
  3. Circle calculator will give the perimeter and area of a circle.

Input : A positive real number or parameter as the radius length of a circle;
Output : Two positive real numbers or variables as the perimeter and area of a circle and corresponding units after that.

How to find the circumference and area of a circleHow to find the circumference and area of a circle

Circumference (Perimeter) of Circle Formula: The circumference of a circle is determined by the following formula $$C=D\times\pi$$ where $D$ is the length of the diameter of the circle and $\pi\approx3.14$.

Circumference (Perimeter) of Circle Formula: The circumference of a circle is determined by the following formula $$C=2\times r\times\pi$$ where $r$ is the length of the radius of the circle and $\pi\approx3.14$.

Area of Circle Formula: The area of a circle is determined by the following formula $$A=r\times r\times\pi=r^2\times \pi$$ where $r$ is the length of the radius of the circle and $\pi\approx3.14$.

What is Area & Perimeter of Circle?

A set of points in a plane equally distanced from a given point $O$ is a circle. The point $O$ is called the center of the circle. The distance from the center of a circle to any point on the circle is called the radius of this circle.A radius of a circle must be a positive real number. The circle with a center $O$ and a radius $r$ is denoted by $c(O,r)$.
The distance around a circle is called the perimeter or circumference of the circle. It is usually denoted by $C$.

How to find the circumference and area of a circle

If all vertices of a polygon belong on a circle, then the polygon is called inscribed. If all sides of a polygon are tangent to a circle, then the polygon is called circumscribed.

Method for finding circumference of circle: Let us inscribe into a circle a regular polygon, for example square. Then double the number of sides of this polygon to get octagon. If we continue the process of doubling the number of sides of regular inscribed polygons, we obtain an infinite sequence of perimeters of regular polygons which increases. This increasing sequence is bounded, since perimeters of all inscribed convex polygons are less than the perimeter of any circumscribed polygon. So, this increasing sequence of perimeters has a certain limit. This limit is the circumference. Hence, the circumference of a circle is the limit of the perimeter of a regular polygon inscribed into the circle when the number of its vertices is doubled indefinitely. Because all circles are similar, the ratio of the circumference to the diameter is the same number for all circles. This ratio of circumference to diameter is denoted by the Greek letter $\pi\approx 3.14$. Thus, the formula for circumference is

How to find the circumference and area of a circle

How to find the circumference and area of a circleHow to find the circumference and area of a circle

The perimeter is measured in units such as centimeters,meters, kilometers, inches, feet, yards, and miles. The area is measured in units such as square centimeters $(cm^2)$, square meters $(m^2)$, square kilometers $(km^2)$ etc.

The Area and perimeter of a circle work with steps shows the complete step-by-step calculation for finding the circumference and area of the circle with the radius length of $8\;in$ using the circumference and area formulas. For any other value for the length of the radius of a circle, just supply a positive real number and click on the GENERATE WORK button. The grade school students may use this circle calculator to generate the work, verify the results of perimeter and area of two dimensional figures or do their homework problems efficiently. They can use these methods in order to determine the area and lengths of parts of a circle.

Real World Problems Using Area and Perimeter of a Circle

Calculating areas and circumferences of circles plays an important role in almost all field of science and real life. For instance, formula for circumference and area of a circle can be applied into geometry. They are used to explore many other formulas and mathematical equations. An arch length is a portion of the circumference of a circle. The ratio of the length of an arc to the circumference is equal to the ratio of the measure of the arc to $360$ degrees. A sector of a circles is the region bounded by two radii of the circle and their intercepted arc.

How to find the circumference and area of a circle

How to find the circumference and area of a circle

Circle Practice Problems

Practice Problem 1:
A pizza is divided into $8$ equal pieces. The diameter of the pizza is $25$ centimeters. Find the area of one piece of pizza.

Practice Problem 2:
Given a tire with diameter of $100$ centimeters. How many revolutions does tire make while traveling $10$ kilometers?

The circle calculator, formula, example calculation (work with steps), real world problems and practice problems would be very useful for grade school students (K-12 education) to understand the concept of perimeter and area of circle. This concept can be of significance in geometry, to find the perimeter, area and volume of solids. Real life problems on circles involving arc length, sector of a circle, area and circumference are very common, so this concept can be of great importance of solving problems.

It is important to know how to do this for any GCSE maths paper. There are two very useful formula but they can be a little confusing to remember. To help you, I have a fun ditty that my maths teacher taught me when I was at school (many moons ago!).

How to find the circumference and area of a circle

Tweedle Dum and Tweedle Dee
Round the circle is Pi times d
If the area is to be declared
Use the formula Pi r squared

Of course, you’ve got to understand what the d and the r represent. Pi is represented as the π symbol. It can either be simplified to something like 3.14 or you can use the π button on your calculator.

Here’s a handy diagram, recapping the component parts of a circle:

How to find the circumference and area of a circle

So in summary, these are the two formula you’d need to know for a GCSE maths exam.

Circumference of a Circle = πd

Area of a Circle = πr 2

All of this can be found on a handy, FREE to download, PDF file that I have created – DOWNLOAD – How to calculate the area and circumference of a circle.

Like this? Read more below…

How to find the circumference and area of a circle

“Think of a Number” Trick – how do you do it?

How to find the circumference and area of a circle

How do you calculate the volume of a pizza?

How to find the circumference and area of a circle

Divisibility Rules

How to find the circumference and area of a circle

About Me

My name is Nicola Bhalerao and I am a private tutor based in Warwick. Since 2013, I have provided one-to-one tuition for children and adults. I specialise in maths tutoring, but cater for different requests, ranging from 11+ to various computing skills, including website training.

My background is in computing, with a Computer Science degree from Warwick University. I have worked many years as a programmer, latterly in the games industry. Both my sons were tutored by me for the 11+ (they went to a local grammar school). I received training for teaching secondary school maths and I am fully CRB checked.

I am a WordPress expert, having spent many years creating numerous websites with my other business, Smiling Panda Web Design. Although I no longer actively work on websites for others, I offer help with understanding / updating / creating your own WordPress website.

Table Of Contents

  1. What Is The Area Of A Circle?
  2. How To Find The Area Of A Circle
    • Area Of A Circle Formula
    • Area Of A Circle Using Diameter
  3. How to Calculate the Area of a Circle
  4. Area Of A Circle Using Circumference
    • Area and Circumference Formula
    • How To Find Area With Circumference

What Is The Area Of A Circle?

A circle is not a square, but a circle’s area (the amount of interior space enclosed by the circle) is measured in square units. Finding the area of a square is easy: length times width.

A circle, though, has only a diameter, or distance across. It has no clearly visible length and width, since a circle (by definition) is the set of all points equidistant from a given point at the center.

Yet, with just the diameter, or half the diameter (the radius), or even only the circumference (the distance around), you can calculate the area of any circle.

How To Find The Area Of A Circle

Recall that the relationship between the circumference of a circle and its diameter is always the same ratio, 3.14159265 , pi, or π . That number, π , times the square of the circle’s radius gives you the area of the inside of the circle, in square units.

Area Of A Circle Formula

If you know the radius, r , in whatever measurement units (mm, cm, m, inches, feet, and so on), use the formula π r 2 to find area, A :

The answer will be square units of the linear units, such as m m 2 , c m 2 , m 2 , square inches, square feet, and so on.

Here is a circle with a radius of 7 meters. What is its area?

[insert drawing of 14-m-wide circle, with radius labeled 7 m]

Area Of A Circle Using Diameter

If you know the diameter, d , in whatever measurement units, take half the diameter to get the radius, r , in the same units.

Here is the real estate development of Sun City, Arizona, a circular town with a diameter of 1.07 kilometers. What is the area of Sun City?

How to find the circumference and area of a circle

First, find half the diameter, given, to get the radius:

1.07 2 = 0.535 k m = 535 m

Plug in the radius into our formula:

A = 899,202.3572 m 2

To convert square meters, m 2 , to square kilometers, k m 2 , divide by 1,000,000 :

Sun City’s westernmost circular housing development has an area of nearly 1 square kilometer!

How to Calculate the Area of a Circle

Try these area calculations for four different circles. Be careful; some give the radius, r , and some give the diameter, d .

Remember to take half the diameter to find the radius before squaring the radius and multiplying by π .

Problems

  1. A 406-mm bicycle wheel
  2. The London Eye Ferris wheel with a radius of 60 meters
  3. A 26-inch bicycle wheel
  4. The world’s largest pizza had a radius of 61 feet, 4 inches (736 inches)

Answers

  1. A 406-mm bicycle wheel has a radius, r , of 203 mm:

A = π × 203 m m 2

A = 637.7433 m m 2

The London Eye Ferris wheel’s 60-meter radius:

A 26-inch bicycle wheel has a radius, r , of 13 inches:

A = 530.9291 i n 2

The world’s largest pizza with its 736-inch radius:

A = π × 736 i n 2

A = 1,701,788.17 i n 2

That is 11,817.97 f t 2 of pizza! Yum! Anyway, how did you do on the four problems?

Area Of A Circle Using Circumference

If you have no idea what the radius or diameter is, but you know the circumference of the circle, C , you can still find the area.

Area and Circumference Formula

Circumference (the distance around the circle) is found with this formula:

That means we can take the circumference formula and “solve for r ,” which gives us:

We can replace r in our original formula with that new expression:

That expression simplifies to this:

That formula works every time!

How To Find The Area With Circumference

Here is a beautiful, reasonable-sized pizza you and three friends can share. You happen to know the circumference of your pizza is 50.2655 inches, but you do not know its total area. You want to know how many square inches of pizza you will each enjoy.

[insert cartoon drawing of typical 16-inch pizza but do not label diameter]

Substitute 50.2655 inches for C in the formula:

A = 50.2655 2 4 π

A = 2,526.6204 4 π

A = 201.0620 in 2

Equally divide that total area for a full-sized pizza among four friends, and you each get 50.2655 i n 2 of pizza! That’s about a third of a square foot for each of you! Yum, yum!

The circumference (perimeter) of a circle is 2πr and its area is πr 2 , where r is the radius of the circle and π is a constant equal to the ratio of circumference of a circle to its diameter.

A great Indian mathematician Aryabhata (476 – 550 AD) gave the value of π which is equal to 3.1416 correct to four places of decimals. However, for practical purposes, the value of π is generally taken as 22/7 or 3.14 approximately.

Circumference of Circle

Wrap a thread around any circular object so that the thread may not be loose and overlap. Measure this by a measuring scale as the thread is linear. This is approximately the circumference of the circular object.

For any circle, the ratio of c/d is same and this is denoted by π.

Circumference / Diameter = π

Circumference = π × Diameter

Circumference of circle = 2 × π × radius

π = 22/7 or π = 3.14

Example 1: Find the circumference of circle when radius is 3.5 cm.

Circumference = 2 × 22/7 × 7/2

Example 2: The radii of two circles are 18 cm and 10 cm. Find the radius of the circle whose circumference is equal to the sum of the circumferences of these two circles.

Let the radius of the circle be r cm. Its circumference = 2πr cm.

Sum of circumferences of the two circles = (2π × 18 + 2π × 10) cm

Therefore, 2πr = 2π × 28

Area of Circle

Area of circle = π × (radius) 2

Example 3: There is a circular path of width 2 m along the boundary and inside a circular park of radius 16 m. Find the cost of paving the path with bricks at the rate of Rs.24 per m 2 . (Use π = 3.14)

Let OA be radius of the park and shaded portion be the path.

OB = 16 m – 2 m = 14 m

Area of the path = (π × 16 2 – π × 14 2 ) m 2

= π(16 + 14)(16 – 14) m 2

= 3.14 × 30 × 2 = 188.4 m 2

So, cost of paving the bricks at Rs.24 per m 2

Calculate the cirumference, radius, diameter and area of a circle

Circumference is basically the length when measured through the boundary of a circle. It is same as the perimeter of other polygons, just that it has a special name called ‘circumference’. This is typically taught among basic maths calculations in schools. It is to be noted that some people falsely call circumference as circumfrence.

Circumference calculator is a free tool used to calculate the circumference of a circle when the radius is given. It can be also used to calculate other parameters of a circle such as diameter, radius and area. This means you can use this tool to do other calculations such as diameter to circumference, radius to area, radius to cicumference, area to radius, area to circumference etc. Infact, all the numbers are shown as soon as you type any one number. This is useful if you need to quickly calculate the circumference for whatever reasons.

How to use?

1. Enter any one value into one of the input fields.
2. This calculator will show the results in other fields

It is quite simple. This is the equation to find the circumference when radius is given

So, Radius = Circumference/(2*Pi)

How to find the circumference and area of a circle

The formula to find the circumference when radius is given is

The formula to find the area when radius is given is

Area of circle = ПЂ*Radius*Radius

In the above formulas, ПЂ=3.14159 and R is the radius. You can read more about circumference in this WikiPedia article – Circumference. Or, if you are a student interested in learning more about circles, circumference, radius and their relation, then Khan Academy’s this page is useful.

In Mensuration the circumference and area of a circle are defined as the length of the boundary of the circle and region occupied by the circle in 2-D Geometry. Let us discuss in detail the area and circumference of the circle using the formulas and solved example problems. We provide a detailed explanation of how to calculate the circumference and area of the circle.

What is Circumference and Area of Circle?

Circumference of Circle:

The circumference of the circle is the measure of the boundary of the circle. The circumference of the circle is also known as the perimeter of the circle. The perimeter or circumference of the circle is measured in units.
C = Πd or 2Πr

Area of Circle:

The area of the circle is the region covered by the circle or sphere in two-dimensional mensuration. The units to measure the area of the circle is square units.
A = Πr²
Where,
A is the area of the circle
r is the radius of the circle

What is the radius of the circle?

The radius of the circle is the distance from the center to the outline of the circle. Radius plays an important role in calculating the area and perimeter of the circle.

Properties of Circle

The properties of the circle are given below,

  • The diameter of the circle is the longest chord of the circle.
  • The circle is said to be congruent if it has the same radii.
  • A circle can confine rectangle, square, trapezium, etc.
  • If the tangents are drawn at the end of the diameter they are parallel to each other.

Area and Circumference of Circle Formula

Circumference:
The circumference of the circle is the measure of the boundary of the circle. The formula for the circumference of the circle is given below,
C = Πd
Where,
C is the circumference of the circle
Π is the mathematical constant
The approximate value of pi is 3.14 or 22/7
d is the diameter of the circle
C = 2Πr
Where,
C is the circumference of the circle
Π is the mathematical constant
The approximate value of pi is 3.14 or 22/7
r is the radius of the circle
Area:
The formula for the area of the circle is as follows,
A = Πr²
A is an area of the circle
Π is the mathematical constant
The approximate value of pi is 3.14 or 22/7
r is the radius of the circle
Area of Semi-Circle:
The area of the semicircle is the region covered by the 2D figure. The formula for the area of the semi-circle is as follows,
A = Πr²/2
Perimeter of the Semi-circle:
The formula for the perimeter of the semi-circle is given below,
P = 2Πr/2 = Πr

Solved Examples on Circumference and Area of a Circle?

Get the step by step explanation on the formula of Area and Circumference of Circle here.

1. What is the circumference of the circle with a radius of 7cm?

Given,
r = 7cm
We know that,
Circumference of the circle = 2Πr
C = 2 × 22/7 × 7 cm
C = 44 cm
Thus the circumference of the circle is 44 cm.

2. What is the circumference of the circle with a diameter of 21 cm?

Given,
d = 21 cm
We know that,
Circumference of the circle = 2Πr
C = Πd
C = 22/7 × 21cm
C = 22 × 3cm
C = 66 cm
Therefore the circumference of the circle is 66 cm.

3. Find the area of the circle with a radius of 14m?

Given,
r = 14m
We know that,
Area of Circle = Πr²
A = 22/7 × 14 × 14 sq.m
A = 22 × 2 × 14 m²
Thus the area of the circle is 616m²

4. Find the area of the circle if its circumference is 124m?

Given,
Circumference of the circle = 124m
We know that,
Circumference of the circle = 2Πr
124m = 2Πr
Πr = 124/2
Πr = 62
r = 62 × 7/22
r = 19.72 m
Now find the area of the circle using the radius.
Area of Circle = Πr²
A = 3.14 × (19.72)²
A = 1221 sq. m
Therefore the area of the circle is 1221 sq. meters.

5. Find the area and circumference of the circle of radius 14m?

Given,
radius = 14m
We know that,
Circumference of the circle = 2Πr
C = 2 × 22/7 × 14m
C = 2 × 22 × 2m
C = 88m
Now find the area of the circle using the radius.
Area of Circle = Πr²
A = Π(14)²
A = 22/7 × 14 × 14 sq.m
A = 22 × 2 × 14
A = 44 × 14 sq.m
A = 616 sq.m
Thus the area of the circle is 616 sq.m

FAQs on Circumference and Area of Circle

1. How to calculate the area of a circle?

The area of the circle can be calculated by the product of pi and radius squared.

2. What is the diameter of the circle?

The diameter of the circle is 2r.

3. How to calculate the circumference of the circle?

The circumference of the circle can be calculated by multiplying the diameter with pi.

The area of a circle is the plane region bounded by the circle’s circumference.

How to find the circumference and area of a circle

The area of a circle can be found using the following formula:

where A is area, r is radius, and π is the mathematical constant approximately equal to 3.14159.

Alternatively, if using the circle’s diameter, D, the area is:

Or, if using the circle’s circumference, C, the area is:

Find the area of circle O below.

How to find the circumference and area of a circle

A = π·8 2 = 64π ≈ 201.06

Area formula proof

The formula for the area of a circle can be proven in a number of ways. One such way involves breaking the circle into equal sectors and rearranging them to construct a parallelogram.

  • In the figure above, the circle with radius r is broken into 16 sectors of equal area. Below the circle, these sectors were rearranged to resemble a parallelogram.
  • The 8 arcs of the shaded sectors form the base of the parallelogram, and represent one-half of the circle’s circumference, C. The height of the parallelogram is the radius, r.
  • The area, A, of a parallelogram is A = bh. So, the area of our parallelogram can be approximated as .
  • Since the circumference of a circle is 2πr, the area of the parallelogram is approximately .
  • The higher the number of sectors we use to break up the circle, the more linear the base of the parallelogram will be. So, the exact value of the area of the circle is πr 2 , given that an infinite number of sectors are used.

A circle is easy to make:

Draw a curve that is “radius” away
from a central point.

All points are the same distance from the center.

How to find the circumference and area of a circle

You Can Draw It Yourself

Put a pin in a board, put a loop of string around it, and insert a pencil into the loop. Keep the string stretched and draw the circle!

Play With It

Try dragging the point to see how the radius and circumference change.

(See if you can keep a constant radius!)

Radius, Diameter and Circumference

The Radius is the distance from the center outwards.

The Diameter goes straight across the circle, through the center.

The Circumference is the distance once around the circle.

And here is the really cool thing:

When we divide the circumference by the diameter we get 3.141592654.
which is the number ПЂ (Pi)

So when the diameter is 1, the circumference is 3.141592654.

Circumference = ПЂ Г— Diameter

Example: You walk around a circle which has a diameter of 100m, how far have you walked?

Distance walked = Circumference = ПЂ Г— 100m

= 314m (to the nearest m)

Also note that the Diameter is twice the Radius:

Diameter = 2 Г— Radius

And so this is also true:

Circumference = 2 Г— ПЂ Г— Radius

Г— 2 Г— ПЂ
Radius Diameter Circumference

Remembering

The length of the words may help you remember:

  • Radius is the shortest word and shortest measure
  • Diameter is longer
  • Circumference is the longest

Definition

The circle is a plane shape (two dimensional), so:

Circle: the set of all points on a plane that are a fixed distance from a center.

The area of a circle is ПЂ times the radius squared, which is written:

  • A is the Area
  • r is the radius

To help you remember think “Pie Are Squared” (even though pies are usually round) :

Example: What is the area of a circle with radius of 1.2 m ?

Or, using the Diameter:

A = ( ПЂ /4) Г— D 2

Area Compared to a Square

A circle has about 80% of the area of a similar-width square.
The actual value is ( ПЂ /4) = 0.785398. = 78.5398. %

And something interesting for you to try: Circle Area by Lines

Names

Because people have studied circles for thousands of years special names have come about.

Nobody wants to say “that line that starts at one side of the circle, goes through the center and ends on the other side” when they can just say “Diameter”.

So here are the most common special names:

Lines

A line that “just touches” the circle as it passes by is called a Tangent.

A line that cuts the circle at two points is called a Secant.

A line segment that goes from one point to another on the circle’s circumference is called a Chord.

If it passes through the center it is called a Diameter.

And a part of the circumference is called an Arc.

Slices

There are two main “slices” of a circle.

The “pizza” slice is called a Sector.

And the slice made by a chord is called a Segment.

Common Sectors

The Quadrant and Semicircle are two special types of Sector:

Quarter of a circle is called a Quadrant.

Half a circle is called a Semicircle.

Inside and Outside

A circle has an inside and an outside (of course!). But it also has an “on”, because we could be right on the circle.

Example: “A” is outside the circle, “B” is inside the circle and “C” is on the circle.

Ellipse

A circle is a “special case” of an ellipse.

Area of a circle is defined as the space occupied by the circular object on a flat surface. The area of a shape can be measured by comparing the shape to squares of a fixed size.

Circumference :

The perimeter of a circle is called its circumference. In other words, t he distance around the edge of a circle.

Formulas for Circumference and Area of a Circle

How to find the circumference and area of a circle

The measurements of perimeter use units such as centimeters, meters, kilometers, inches, feet, yards, and miles. The measurements of area use units such as square centimeters (cm 2 ), square meters( m 2 ), and so on.

An irrigation sprinkler waters a circular region with a radius of 14 feet. Find the circumference of the region watered by the sprinkler. Use 22/7 for ПЂ.

Use the formula.

Substitute 14 for r.

Substitute 22/7 for ПЂ.

C ≈ 2 x (22/7) x 14

C ≈ 2 x (22/1) x 2

So, the circumference of the region watered by the sprinkler is about 88 feet.

The diameter of a car wheel is 21 inches. Find the circumference of the wheel.

Radius = Diameter / 2

Radius = 21/2 inches

Use the formula.

Substitute 21/2 for r.

Substitute 22/7 for ПЂ.

C ≈ 2 x (22/7) x (21/2)

C ≈ 2 x (11/1) x (3/1)

So, the circumference of the wheel is 66 inches.

Find the diameter, radius, circumference and area of the circle shown below. use 3.14 as an approximation for ПЂ .

How to find the circumference and area of a circle

From the diagram shown above, we can see that the diameter of the circle is

The radius is one half the diameter. So, the radius is

r = d/2 = 8/2 = 4 cm

Using the formula for circumference, we have

C = 2 πr ≈ 2(3.14)4

Using the formulas for area, we have

A = πr 2 ≈ (3.14)(4) 2

A ≈ 50.24 square cm.

A biscuit recipe calls for the dough to be rolled out and circles to be cut from the dough. The biscuit cutter has a radius of 4 cm. Find the area of the top of the biscuit once it is cut. Use 3.14 for ПЂ.

Since the top of the biscuit is in the shape of a circle, we can use area of circle formula to find area of the top of the biscuit.

Area of a circle = ПЂr 2

Radius is given in the question. That is 4 cm.

Substitute 4 for r in the above formula.

Area of the circle = ПЂ(4) 2

Since radius is not a multiple of 7, we can use π ≈ 3.14.

Area of the circle ≈ (3.14) x (4) 2

Area of the circle ≈ 3.14 x 16

Area of the circle ≈ 50.24 square cm.

The area of the biscuit is about 50.24 square cm.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

To understand how to calculate square footage we must first begin with the definition of area. An area is the size of a two-dimensional surface. The area of a circle is the space contained within its circumference (outer perimeter). To find out the area of a circle, we need to know its diameter which is the length of its widest part. The diameter should be measured in feet (ft) for square footage calculations and if needed, converted to inches (in), yards (yd), centimetres (cm), millimetres (mm) and metres (m).

The formula:
Area of a Circle = π x (Diameter/2)^2
π = 3.142
Answer = (π x (Diameter/2)^2) square area
Abbreviations of unit area: ft 2 , in 2 , yd 2 , cm 2 , mm 2 , m 2

Where do you need it in daily life?

Our Square Footage Calculator helps you calculate the area required for making circular landscaping designs, carpeting, wall decals, centre moulding on a ceiling and floor tiling.

Easily Find The Area Of A Circle (And Related Use Cases)

Technology has advanced and with that, there have been many calculators which help users precisely measure things even from the comfort of their laptop or mobile phone. Our area of circl calculator lets you easily find the area, circumference, radius or specific diameter of any circle.

All you need to do is fully understand the variables of this formula including the:

  • r (radius)
  • d (diameter)
  • C (circumference)
  • A (area)
  • π = pi = 3.1415926535898
  • √ = square root

With any of these variables (A, C, r or d) of a circle, you can precisely measure the other three unknowns. You can use this formula in many real world examples such as when building a house, drilling, filling holes with concrete etc. Essentially, the formula gives you accurate details on how much material you need or how big the surface (you will drill into) needs to be.

However, you should also be aware that the area of a circle calculator demands other things which you need to know before measuring.

Things You Need To Take Care About Measuring An Area Of A Circle.

Circles are complex shapes. Perhaps, their main variable is the radius – which is measured from the center of the circle to any of its sides. Essentially, the diameter is twice the radius – or any line that goes from one side of the circle to the other while crossing its center.

The circumference of a circle, however, is not that commonly understood by many. Essentially, this variable can be defined as the distance around the circle or the entire length of the circuit along the circle.

The π (pi) variable is basically a constant which cannot be expressed as a fraction but applies to all calculations – including the area of a circle calculator – whereas the √ (square foot) is basically the total surface within a circle.

Used since ancient geometrics, all of these variables let you precisely calculate anything related to a circle. However, instead of doing things manually, now you can use our area of a circle calculator and make use of the ready circle formula.

Solve the Common Geometry Problem Today With Our Area Of A Circle Calculator.

Whether you are in class solving a math test or need an accurate calculation about the area of a circle for a project that you are building, the formula for area of a circle is simple – but not that simple when you are left with a pen and paper.

This is why and how our Area Of A Circle Calculator can help you and instantly solve your questions. All you need is another variable to get the other three and solve the problem immediately.

Now, you can finally use and apply the Area Of A Circle calculator everywhere – and quickly get to the information you need – without going in circles!

What measurements do you need?

You need to know the diameter of the circle in either feet (ft), inches (in), yards (yd), centimetres (cm), millimetres (mm) or metres (m).

What can you calculate with this tool?

You can calculate the area of the circle border in square feet, in square inches, square yards, square centimetres, square millimetres and square meters. Yes, our tool is that awesome.

Our calculator gives you the option of calculating the exact cost of materials. All you have to do is enter the price per unit area and voila, you have the total cost of materials in a single click!

Conversion factors:

To convert among square feet, square inches, square yards, square centimetres, square millimetres and square meters you can utilize the following conversion table.

Square feet to square yards multiply ft 2 by 0.11111 to get yd 2
Square feet to square meters multiply ft 2 by 0.092903 to get m 2
Square yards to square feet multiply yd 2 by 9 to get ft 2
Square yards to square meters multiply yd 2 by 0.836127 to get m 2
Square meters to square feet multiply m 2 by 10.7639 to get ft 2
Square meters to square yards multiply m 2 by 1.19599 to get yd 2
Square meters to square millimetres multiply the m 2 value by 1000000 to get mm 2
Square meters to square centimetres multiply the m 2 value by 10 000 to get cm 2
Square centimetres to square metres multiply the cm 2 value by 0.0001 to get mm 2
Square centimetres to square millimetres multiply the cm 2 value by 100 to get mm 2
Square millimetres to square centimetres multiply the mm 2 value by 0.000001 to get cm 2
Square millimetres to square metres multiply the mm 2 value by 1000000 to get m 2

How to find the circumference and area of a circle

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Whenever you will read about the properties, you will come across the term square footage as it is an imperial unit that indicate.

How to find the circumference and area of a circle

World’s Most Sophisticated Buildings and Total Area In Square Footage

The world’s most prestigious buildings can be a great inspiration for architects and designers. The same goes for the tourists as.

How to find the circumference and area of a circle

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Howdy readers, today you will learn how to write a program to calculate area and circumference of a circle using C++ Programming language.

How to find the circumference and area of a circle

This program prompts the user to enter the radius of a circle, then it calculates the area and circumference of the circle using the following formulas:

  • Circumference of circle = 2 x π x radius
  • Area of circle = π x radius x radius

We will use the following methods to find the area and circumference of the circle.

  1. Using Standard Method
  2. Using User-defined Functions

So, without any delay, let’s begin this tutorial.

Table of Contents

C++ Program to Calculate Area and Circumference of Circle

C++ Program

Output

How to find the circumference and area of a circle

Explanation

In the above program, we have declared four float data type variables named radius, area, perimeter and PI.

This program prompts the user to enter the radius of the circle. This value gets stored in the ‘radius‘ named variable.

Area of the circle is calculated using the formula, Area = πr 2 , where ‘r’ is the radius of the circle.

Similarly, the circumference of the circle is calculated using the formula, circumference = 2πr, where ‘r’ is the radius of the circle.

Finally, the area and the circumference of the circle is printed on the screen using the cout statement.

C++ Program to Calculate Area and Circumference of Circle Using Functions

C++ Program

Output

How to find the circumference and area of a circle

Conclusion

I hope after reading this post, you understand how to write a program to calculate area and circumference of a circle using C++ Programming language.

If you face any difficulty understanding this program, then let us know in the comment section. We will be glad to solve your queries.

Here is the answer to questions like: how to find the area of a circle with circumference 16 pi inches?

Circle Calculator

Use the this circle area calculator below to find the area of a circle given its circumference, or other parameters. To calculate the area, you just need to enter a positive numeric value in one of the 3 fields of the calculator. You can also see at the bottom of the calculator, the step-by-step solution.

Formula for area of a circle

Here a three ways to find the area of a circle (formulas):

Circle area formula in terms of radius

Circle area formula in terms of diameter

Circle area formula in terms of circumference

See below some definitions related to the formulas:

Circumference

Circumference is the linear distance around the circle edge.

Radius

The radius of a circle is any of the line segments from its center to its perimeter. The radius is half the diameter or r = d 2 .

Diameter

The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. The diameter is twice the radius or d = 2·r .

The Greek letter π

π represents the number Pi which is defined as the ratio of the circumference of a circle to its diameter or π = C d . For simplicity, you can use Pi = 3.14 or Pi = 3.1415. Pi is an irrational number. The first 100 digits of Pi are: 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 .

If you input the radius in centimeters, you will get the answer in square centimeters (cm²), if in inches, will get the answer in square inches (in²) and so on .

Circumference is often misspelled as circunference.

To convert area into circumference, take the two formulas for circles–circumference and area:

Now, isolate the common variable (r) in the second equation.

Now you can substitute this in for “r” in the first equation to find circumference

C=2pi*sqrt(36pi/pi) pi cancels out

Add your answer:

What is the circumference of a 36 circle?

The circumference of a 36 circle is: 113.1 (diameter x pi = circumference).

How is pi in relation to a circle?

Pi is related to the area and the circumference of the circle. The area is Pi multiplied by the radius of the circle squared and the circumference is Pi times the diameter of the circle. if you’re wondering how it works, pi is the area of a circle with radius of 1 (unit), and the circumference of a circle with a radius of ½ (unit).

If a circle has a diameter of 36 what is the circumference?

pi x diameter gives you the circumference. pi x 36 = ? I don’t have my calculator on me.

What is the circumference and area when radius 9in and d 7.3?

Circumference of a circle = 2*pi*radius or pi*diameter Area of a circle = pi*radius2

Area of a circle with a 12 inch circumference?

The circumference of a circle is given by Circumference = pi x diameter. The area of a circle is given by Area = pi/4 x diameter2. Thus for a circle with circumference c = 12 in. The area will equal a = 11.459 in2.

C program to find diameter, circumference, and area of a circle; Through this tutorial, we will learn how to find or calculate the diameter, circumference and area of a circle using the formula, function, and math modules in c programs.

Programs and Algorithm to Find the Area of a Circle

  • Algorithm To Find Diameter, Circumference, and Area of a Circle
  • C Program to Find Diameter, Circumference, and Area of a Circle using Formula
  • C Program to Find Diameter, Circumference, and Area of a Circle using Function
  • C Program to Find Diameter, Circumference, and Area of a Circle using Math Module

Algorithm To Find Diameter, Circumference, and Area of a Circle

Use the following algorithm to write a program to find diameter, circumference and area of a circle; as follows:

  1. START PROGRAM.
  2. TAKE RADIUS AS INPUT FROM USER.
  3. FIND AREA OF DIAMETER, CIRCUMFERENCE, CIRLCE USING THE FOLLOWING FORMULAS:
    1. diameter = 2 * radius;
    2. circumference = 2 * PI * radius;
    3. area = PI * radius * radius;
  4. PRINT “AREA OF CIRCLE, DIAMETER, CIRCUMFERENCE “
  5. END PROGRAM.

C Program to Find Diameter, Circumference, and Area of a Circle using Formula

The output of the above c program; as follows:

C Program to Find Diameter, Circumference, and Area of a Circle using Function

The output of the above c program; as follows:

C Program to Find Diameter, Circumference, and Area of a Circle using Math Module

The output of the above c program; as follows:

Lesson Plan

Circumference and Area of a Circle

Grade Levels

Course, Subject

Keywords

Vocabulary

  1. Diameter- The distance across a circle through the center.
  2. Radius- The distance from the center of a circle to any point on the circle.
  3. Circumference- The distance around the circle.
  4. Area- The amount of surface covered by a figure.

Objectives

This lesson will teach students how to calculate the circumference and area of a circle and how to apply this knowledge to different situations.

  1. The students will be able to calculate the circumference of a circle.
  2. The students will be able to calculate the area of a circle.

Lesson Essential Question(s)

What are the unique characteristics of circles and their related parts?

Duration

One class period

Materials

  • Yarn
  • Rulers
  • Scissors
  • Circles of various sizes
  • Calculators
  • Hula Hoops
  • Book- Sir Cumference and the Dragon of Pi
  • http://illuminations.nctm.org/Lessons/ApplePi/ApplePi-AS-Record.pdf. “Apple PI” Illuminations. Thinkfinity.org. Web. 3 Mar, 2010. .
  • http://nrich.maths.org/2883 “Virtual Geoboard” nrich Web. 3 Mar, 2010. http://nrich.maths.org.
  • Circumference and Area of Circles.doc

Suggested Instructional Strategies

This lesson utilizes a variety of instructional practices such as active engagement, visual, tactile, kinesthetic, musical, rhythmic, simulation, and visual/spatial strategies. Students actively participating in a variety of activities to engage and enhance learning.

Instructional Procedures

WHERETO

W

The teacher will tell the students that today they are going to be learning about the circumference and area of circles. The teacher will review the parts of a circle with the students. A virtual geoboard will be used as a formative assessment to review the parts of a circle: http://nrich.maths.org/content/id/2883/circleAngles.swf. Based on student responses, the teacher may compact the curriculum and advanced to the new concepts or review/reteach the vocabulary as necessary. The teacher will then review that perimeter is the distance around a polygon and circumference is the distance around a circle. The teacher will provide the students with a real-life scenario involving putting up a fence around a circular swimming pool. She will ask the students how they could calculate the distance around the pool. This will lead into a discussion about possible ways to calculate circumference. The teacher will explain that during today’s lesson the students will be given the opportunity to calculate the circumference and area of a plethora of circles.

H

When the students enter the classroom there will be hula hoops randomly placed on the floor. The hula hoops will be used to help spark interest and conversation in today’s topic of discussion- circumference and area of circles.

E

The teacher will divide the students into small groups. Each group will be provided with a hula hoop, yarn, ruler, and scissors. The students will use these resources to come up with a way to calculate the circumference of the hula hoop. The students will be given the opportunity to share their results and method used to calculate the circumference.

R

The teacher will then have the students investigate the ratio of circumference to the diameter of a circle. He/she will provide the students with circles of various sizes, yarn, scissors and rulers. The students will measure the distance around each circle with yarn. The students will also measure the distance across each circle. They will record their results on Illuminations Apple Pi worksheet http://illuminations.nctm.org/Lessons/ApplePi/ApplePi-AS-Record.pdf. The students will divide the circumference by the diameter to find the ratio of circumference to the diameter of a circle. The students will be able to see that the circumference is a little over three times bigger than the diameter. The value of PI will be introduced at this time- 3.14. The teacher will read the book Sir Cumference and the Dragon of Pi to the students to help reinforce the value of PI. The students will discuss the meaning of the poem “The Circle’s Measure” found in the story. The teacher will then introduce the students to the formula for circumference. The students will practice using the formula to find the circumference of various circles provided by the teacher. The teacher will ask the students what they would need to calculate if they want to find the amount of surface covered by a circle (area). The teacher will introduce the students to the formula for area of a circle. She will remind the students that area is always in square units. The students will practice finding the area of various circles.

The Circle’s Measure

Measure the middle circle around,

Divide so a number can be found.

Every circle, great and small-

The number is the same for all.

It’s also the dose, so be clever.

Or a dragon he will stay.

E

The students will revisit the original problem of putting a fence around a circular pool. The students will use the knowledge they have gained from this lesson to calculate the fencing needed for a pool with a diameter of 15 feet. They will also need to calculate the area of the pool to determine what size solar cover they would need to purchase for the pool.

T

Cooperative learning and calculators will be used to assist the students with this lesson. Based on formative assessment information, the teacher will adjust instructional practices and provide remediation and reteaching as necessary. By design, this lesson incorporates and addresses numerous learning stules via poems, stories, tactile, kinesthetic, visual, auditory, and real world application scenarios. These different methodologies allow for differentiateion to meet student needs. Additionally, the following website may be used to provide extra practice or enrichment as needed: http://www.pdesas/module/content/resources/3165/view/ashx

O

As a summative assessment, each child will be given an individual worksheet on circumference and area of circles. Circumference and Area of Circles.doc The students will independently calculate the circumference/area of each circle. The teacher will monitor and re-teach as necessary.

Formative Assessment

The students will independently complete a circumference and area worksheet. See attached worksheet.

Calculate the radius, arc length, sector areas, and more.

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How to find the circumference and area of a circle

A circle is a two-dimensional shape made by drawing a curve that is the same distance all around from the center. Circles have many components including the circumference, radius, diameter, arc length and degrees, sector areas, inscribed angles, chords, tangents, and semicircles.

Only a few of these measurements involve straight lines, so you need to know both the formulas and units of measurement required for each. In math, the concept of circles will come up again and again from kindergarten on through college calculus, but once you understand how to measure the various parts of a circle, you’ll be able to talk knowledgeably about this fundamental geometric shape or quickly complete your homework assignment.

Radius and Diameter

The radius is a line from the center point of a circle to any part of the circle. This is probably the simplest concept related to measuring circles but possibly the most important.

The diameter of a circle, by contrast, is the longest distance from one edge of the circle to the opposite edge. The diameter is a special type of chord, a line that joins any two points of a circle. The diameter is twice as long as the radius, so if the radius is 2 inches, for example, the diameter would be 4 inches. If the radius is 22.5 centimeters, the diameter would be 45 centimeters. Think of the diameter as if you are cutting a perfectly circular pie right down the center so that you have two equal pie halves. The line where you cut the pie in two would be the diameter.

Circumference

The circumference of a circle is its perimeter or distance around it. It is denoted by C in math formulas and has units of distance, such as millimeters, centimeters, meters, or inches. The circumference of a circle is the measured total length around a circle, which when measured in degrees is equal to 360°. The “°” is the mathematical symbol for degrees.

To measure the circumference of a circle, you need to use “Pi,” a mathematical constant discovered by the Greek mathematician Archimedes. Pi, which is usually denoted with the Greek letter π, is the ratio of the circle’s circumference to its diameter, or approximately 3.14. Pi is the fixed ratio used to calculate the circumference of the circle

You can calculate the circumference of any circle if you know either the radius or diameter. The formulas are:

C = πd
C = 2πr

where d is the diameter of the circle, r is its radius, and π is pi. So if you measure the diameter of a circle to be 8.5 cm, you would have:

C = πd
C = 3.14 * (8.5 cm)
C = 26.69 cm, which you should round up to 26.7 cm

Or, if you want to know the circumference of a pot that has a radius of 4.5 inches, you would have:

C = 2πr
C = 2 * 3.14 * (4.5 in)
C = 28.26 inches, which rounds to 28 inches

The area of a circle is the total area that is bounded by the circumference. Think of the area of the circle as if you draw the circumference and fill in the area within the circle with paint or crayons. The formulas for the area of a circle are:

A = π * r^2

In this formula, “A” stands for the area, “r” represents the radius, π is pi, or 3.14. The “*” is the symbol used for times or multiplication.

A = π(1/2 * d)^2

In this formula, “A” stands for the area, “d” represents the diameter, π is pi, or 3.14. So, if your diameter is 8.5 centimeters, as in the example in the previous slide, you would have:

A = π(1/2 d)^2 (Area equals pi times one-half the diameter squared.)

A = 56.71625, which rounds to 56.72

A = 56.72 square centimeters

You can also calculate the area if a circle if you know the radius. So, if you have a radius of 4.5 inches:

A circle is a simple geometrical shape. A circle is a set of all points in a 2D plane that are at a given distance from a given point called centre. A circle can be uniquely identified by it’s center co-ordinates and radius.

  • Center of a Circle is a point inside the circle and is at an equal distance from all of the points on its circumference.
  • Radius is the length of the a segment joining the centre of the circle to any point on the circle.
  • Diameter is the length of the a segment passing through centre of the circle and joining two points on edge. Diameter is twice of Radius.

How to find the circumference and area of a circle
The area of circle is the amount of two-dimensional space taken up by a circle. The area of a circle can be calculated by placing the circle over a grid and counting the number of squares that circle covers. Different shapes have different ways to find the area.
We can compute the area of a Circle if you know its radius.

Area of Circle = PI X Radius X Radius.
Where PI is a constant which is equal to 22/7 or 3.141(approx)
Area is measured in square units.

Circumference is the linear distance around the edge of a circle. It is the length of the curved line which defines the boundary of a circle. The perimeter of a circle is called the circumference.

We can compute the circumference of a Circle if you know its radius.

  • Circumference or Circle = 2 X PI X Radius

We can also compute the circumference of a Circle if you know its diameter.

  • Circumference or Circle = PI X Diameter

C Program to find the area of the circle

How to find the circumference and area of a circle

In above program, we first take radius of a circle as an input from user using scanf function and store it in floating point variable named “radius”. Now, we calculate the area of circle(PI X radius X radius) and store it in variable area. Then we print the area of circle on screen using printf function.

Program Output

C Program to find the area of a circle using pow function

We can use pow function of math.h header file to calculate Radius^2(Radius square) instead of multiplying Radius with itself. double pow(double a, double b) returns a raised to the power of b (a^b). Below program uses pow function to calculate the area of circle.

How to find the circumference and area of a circle

Program Output

C Program to calculate circumference of the circle

Below program calculates the circumference of a circle by taking radius of circle as input from user. We can also find circumference of a circle from diameter, as diameter of a circle is twice of radius.

Below program first take radius of a circle as input from user and then calculate circumference(perimeter) of a circle as 2 X PI X Radius. It then prints the result on screen using printf function.

How to find the circumference and area of a circle

Program Output

Properties of Circle

  • Diameter is the longest chord of a circle.
  • A triangle inside a semi-circle with diameter as one site is always a right angles triangle.
  • A tangent to a circle is at right angles to the radius at the point of intersection.
  • The length of arc of a circle is proportional to the angle subtended by the arc at the center.
  • The equation of a circle whose center is at (0,0) and radius R is x 2 + y 2 = R 2 .

Lets write a C program to calculate area and circumference or perimeter of a Circle using pointer and function.

Video Tutorial: C Program To Find Area and Circumference of Circle using Pointer

Source Code: C Program To Find Area and Circumference of Circle using Pointer

Output 1:
Enter radius of Circle
5

Area of Circle = 78.50
Perimeter of Circle = 31.40

Output 2:
Enter radius of Circle
14

Area of Circle = 615.44
Perimeter of Circle = 87.92

Logic To Find Area and Circumference of Circle using Pointer

We ask the user to enter value for radius of a Circle. We pass this value along with address of variables area and perimeter to the function area_peri().

We copy the value of radius to a local variable r and then we take 2 floating point pointer variables *a and *p. *a represents the value present at address a or &area. *p has value present at address p or &perimeter.

Inside area_peri() function we calculate the area and circumference / perimeter of Circle and store it as value present at addresses a and p. Since a points to address of variable area and p points to address of variable perimeter, the values of variable area and perimeter changes too.

*a = 3.14 * r * r;

*p = 2 * 3.14 * r;

Area and Circumference of Circle

We’ve separate video tutorials to calculate area and circumference of a Circle using radius, and without using pointer and function. You can check them out at these links:

Note: When * is precedes any address, it fetches the value present at that address or memory location.

For list of all c programming interviews / viva question and answers visit: C Programming Interview / Viva Q&A List

For full C programming language free video tutorial list visit:C Programming: Beginner To Advance To Expert

Find the area of a circle with radius, diameter and circumference

Circle

A circle is a simple shape that is the set of all points that are a fixed distance from a given point. A circle can be drawn with a compass or pen, or it can be described algebraically. The distance from a fixed point in a plane to a given point is called a radius. A circle is a special type of a sphere. The fixed point is called the center of the circle. The distance from a point on a circle to the center is called the radius of the circle. The distance from a point on a circle to a line that is not part of the circle is called the diameter of the circle. A circle with a radius of one is called a unit circle. It is a convenient way of representing a circle in Euclidean geometry. Any circle that is not a unit circle is called a non-unit circle.

Area of a Circle

The area of a circle is defined as the amount of space it takes to completely surround the circle. It is calculated by the equation A = ПЂr2, where A is the area, r is the radius, and ПЂ is the constant pi (approximately 3.14159). The formula can be rearranged to find the radius of a circle if you know its area. Area of a circle = ПЂ times the square of the radius.

Area of Circle formula

Given the radius of the circle, the area is the radius squared times pi. Given pi is 3.14159, it would be written as: area=r2*pi

◉ Area of a circle with radius.

Area of circle = ПЂ(r)ВІ = ПЂ(radius)ВІ

◉ Area of a circle calculator with diameter

Area of circle = ПЂ(D/2)ВІ = ПЂ(dimater/2)ВІ

◉ Area of a circle with circumference

Area of circle = CВІ/4ПЂ = circumferenceВІ/4ПЂ

Real example of used area of circle

◉ When calculating the area of a circle, the formula is pi x radius squared. Yes, pi is a complicated number. The truth is, though, that if you want to find the area of a circle you will need to know pi. When you’re calculating the area of a pizza, for example, you will need to figure the diameter of the pizza, and then multiply that by pi. The same is true for the area of a cake or any other round object. To determine the area of a circular object, you will need to measure the diameter of the circle. Once you have the diameter, you will need to use the formula for the area of a circle. The formula is pi x diameter squared.

How to use area of a circle calculatorвќ“

◉ Given a radius of a circle, the formula for finding its area is A = ПЂr2. It is a powerful tool for calculating how much area a circle takes up. For example, a circle with a radius of 10 meters can be found by entering 10 for the radius value. By doing so, the area is calculated to be 314.16 square meters. If you don’t know the radius of a circle, there is a formula for that as well. If you know the diameter of the circle, just divide diameter by two to obtain the radius. The formula for area of circle with diameter d is A = ПЂd2/4 When using the above formula.

How to solve area of circle вќ“

Example.1:-The radius of a circle is 10 cm, find its area?

Answer:- Area = ПЂrВІ = 22/7 * (10)ВІ = 314.15 cmВІ.

Example.2:-The circumference of a circle is 20 cm, find it’s area ?

Answer:- Circumference of circle = 2ПЂr = 20 cm

Area = ПЂrВІ = ПЂ * (10/ ПЂ)ВІ = 100/ПЂ = 31.83 cmВІ.

Example.3:-The diameter of a circle is 20cm, find it’s area?

Answer:- diameter = radius/2 ⇨ radius = diameter/2 = 20/2 = 10 cm.

Area = ПЂrВІ = ПЂ * (10)ВІ = 314.15 cmВІ.

Example.4:-Area of 12 inch radius of a circle,

Answer:- Area of a circle = ПЂ(radius)ВІ = 22/7 * (12)ВІ = 452.38934 inchВІ.

Enter radius value
5

Diameter of Circle = 2 x radius of circle

circumference of Circle = 2 x 3.14 x radius of circle.

Area of circle = 3.14 x (radius of circle) 2

D = Diameter of circle

C = Circumference of circle

A = Area of circle

r = radius of circle

pi( π) = 3.142., which is constant

1. Take the radius in the form of input from user says in radius variable

2. Apply the above formulae and keep the result in required variable.

3. Finally, prints the resultant values of diameter, circumference and area of the circle in the respective variables.

Full Code to Calculate the diameter, circumference and area of circle.

\n is an escape sequence used to change the line in c language.

%f is used as a format specifier because we need to enter float value as value of pi is 3.14. Thus, the resultant value of circumference and area of the circle could be of float value . Therefore, we use %f format specifier.

Please write this code on your own and Run this code and put the values of radius different and see the output of the diameter, circumference and area of circle every time and comment your answer with input and output value.

As, everything is clear in the code, I hope you will be able to write a program how to find the diameter, circumference and area of rectangle in C language. If you have any query related to the above code or with this post. You are always welcome to post your query in the comment box!

find the circumference of the circle round to the nearest foot.

I got a but I’m not sure.
A.132ft
B.264ft
C.1,320FT
D.2,640FT

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What is the diameter?

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not sure. All I got was a line with 42 ft with a dot in the middle

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That’s probably the diameter. Let’s see if it works.

C = pi * d
C = 3.14 * 42
C = 131.88

Thar rounds to 132 feet. You’re right.

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For connexus students the answers are

I got a 5/5 100%
And just for more further proof:

Lesson 7: Circumference of a Circle CE 2015
Essential Math 6 B Unit 3: Geometry and Measurement

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Thank you so much Lola! Winged Dragon Of Ra

For connexus students the answers are

I got a 5/5 100%
And just for more further proof:

Lesson 7: Circumference of a Circle CE 2015
Essential Math 6 B Unit 3: Geometry and Measurement

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Lola is correct. If you are from connexus, listen to Lola’s answers. :)))))))-Warrior Cat Lover

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dude you copied and pasted Lola’s stuff not cool. Thhx LOLA GOT 5/5
:p YESSSAAA

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thanks I just got 100% on it your the best 🙂

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yes thank you but how did you get those answers

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Thank you soo much lola.

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wrong one for me but uh thanks i guess.

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Thank you, Lola! Have a blessed day! 😊💝🙏
-🐺(A Wolf)

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thanks Lola you’re the best! BTW who from 2021-2022? LOL >XD

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thanks howdy your ugly duckling

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LOLA GO ME ALLLLLL OF THEM WRONG

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Example

Calculate the perimeter of a circle

Definition of a circle

A circle is a closed shape formed by tracing a point that moves in a plane such that its distance from a given point is constant.
When a set of all points that are at a fixed distance from a fixed point are joined then the geometrical figure obtained is called circle.
Radius is the fixed distance between the center and the set of points. It is noted “r”.
Diameter is a line segment, having boundary points of circles as the endpoints and passing through the center.

The perimeter of a circle is calculated using the formula 2 x Pi x Radius, or Pi x Diameter.
Diameter = 2 x Radius
The radius of a circle is the length of the line from the center to any point on its edge. The diameter is defined as twice the length of the radius of a circle. The diameter is the distance from one point on a circle through the center to another point on the circle.

The perimeter is defined as the circumference of the circle. The circumference of a circle is the length of the curve that encloses that circle.

Differences between a circle and a disc

Circumference of a circle

The circumference of a circle is the distance around the outside of the circle. A circle’s outside boundary is called the circumference. It is like the perimeter of other shapes like squares. The circumference of a circle is the length of the curve that encloses that circle.

How to find the circumference of a circle?

Calculate the circumference of a circle with the radius

Calculate the circumference of a circle with the diameter

Multiply the diameter by ПЂ (pi is approximately 3.14). It is done, you found the circumference of the circle.

Circles are common shapes. You can see them everywhere—wheels on cars, compact discs with data, frisbees that pass through the air. All these things are circles.

Circles are \(2-dimensional\, figures\), just like quadrilaterals and polygons.

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Video Transcription

However, a circle is measured differently than all the other shapes.

We even need to use a few different terms for describing them. Let’s look at these interesting shapes.

First: Properties of Circles. Circles represent sets of points that are all at the same distance from a fixed, central point.

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We call this fixed, middle point the center. And the distance from the circle’s center to all points on our circle is what we call the radius.

And when we put two radii (the plural form of radius) together and form one line segment across the entire circle, we have the diameter. Diameters of circles pass through the center point of our circle and have their endpoints on that circle itself.

So we see that a circle’s diameter is two \((2)\) times the circle’s radius’ length. We can represent that by the expression \(“2r”\), or \(“2\, times\, its\, radius”\). So if we know the radius of a circle, we multiply it by two \((2)\) and come up with its diameter. This also means that, if we know the diameter of a circle, we may divide by \(2\) (two) to discover its radius.

For example:

The problem: Find this circle’s diameter.

\(d = 2r\) The circle’s diameter is \(2\) (two) times its radius \((or \,2r\)).
\(d = 2(7)\) This circle’s radius is seven \((7)\) inches.
\(d = 14\) So the diameter of our circle is \(2(7)\), or \(14\) inches.

The answer is: This the diameter of our circle is \(14\) inches.

One more example:

The Problem: Find this circle’s radius.

The circle’s radius is half its diameter, or \(\frac<1><2>\,d \).

This circle’s diameter is \(36\) feet, so its radius is \(\frac<1><2>\,(36) = 18\) feet.

The answer is:
The circle’s radius is \(18\) feet.

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Help the child unleash their best yet with our free area and circumference of a circle worksheets. Progressing through tasks like finding the area and circumference, finding the area from the circumference, and finding the circumference from the area, children run a complete course in the quest to fulfill their practice aspirations. Every resource presents a new challenge so each time the learning feels riveting. Our pdf circumference and area of circles worksheets are available in both customary and metric units.

We recommend these printable tools for grade 6, grade 7, and grade 8 students.

Remind students that the formula for the circumference of a circle is 2πr and the formula for the area of a circle is πr². If they have the diameter given, they should use its half in the formulas to determine both the measures.

How to find the circumference and area of a circle

Give 6th grade and 7th grade students a strenuous brain workout with this free circumference and area of circles worksheet! Be sure they round the answer to the nearest tenth so in the long run, working out the two measures will be a no-brainer!

How to find the circumference and area of a circle

Whet your learners’ appetite for more learning-and-practice enthusiasm using this printable worksheet! Watch them get everything right by dividing the circumference by 2π to obtain the value of r and by using it to find the area of the figure.

How to find the circumference and area of a circle

When prepping turns all-round, children will fire on all cylinders! Then finding the area from the circumference will be a hoot! Instruct them to use the circumference to find the radius and calculate the area of the circle with the value of r.

How to find the circumference and area of a circle

If the area of a circle = 12.56 sq. units, what is the circumference? Since the area = πr², 12.56 = 3.14 * r². Divide the area by 3.14 to get r², and take the square root of r. Plug the obtained value in the appropriate formula to find the circumference.

How to find the circumference and area of a circle

Task grade 7 and grade 8 students with finding the circumference given the area. This pdf area and circumference worksheet contains circles with an area of four or five digits, so the mighty math wizards are up against an exciting challenge!

What is Circumference?

Circumference is the distance around a circle. We can find the circumference using either the diameter or radius of a circle.

How to find the circumference and area of a circle

For shapes made of straight lines, we say they have a perimeter. For circles, the perimeter gets the name circumference.

It does not matter if the circle is a slice of a sphere (like earth’s equator) or flat like King Arthur’s gathering place for all his knights if we know either the diameter or the radius, we can find the circumference of a circle. I bet King Arthur would have welcomed Sir Cumference to his Round Table.

Table Of Contents

  1. What is Circumference?
  2. Parts of a Circle
  3. Circumference Formula
    • Diameter To Circumference
    • Radius To Circumference Formula
  4. How To Find Circumference
  5. Find Diameter From Circumference
  6. Find Radius From Circumference

Parts of a Circle

A circle (the set of all points equidistant from a given point) has many parts, but this lesson will focus on three:

  1. Circumference — The distance around the circle (the perimeter of a circle).
  2. Diameter — The distance from the circle through the circle’s center to the circle on the opposite side. (twice the radius)
  3. Radius — The distance from the center of a circle to the circle (half the diameter). Draw a line segment from the center of the circle to any part of the circle and you have the radius.

Circumference Formula

Two formulas are used to find circumference, C , depending on the given information. Both circumference formulas use the irrational number Pi, which is symbolized with the Greek letter, π . Pi is a mathematical constant and it is also the ratio of the circumference of a circle to the diameter.

How to find the circumference and area of a circle

Diameter To Circumference

If you are given the circle’s diameter, d , then use this circumference of a circle formula:

Radius To Circumference Formula

If you are given the radius, r, you can still find the circumference. If you know the radius, the circumference formula is:

You can always find the circumference of a circle as long as you know the diameter or the radius.

How To Find Circumference

Here we have a circle with a given diameter of 12,756.274 k i l o m e t e r s :

To find its circumference, multiply that measurement times π :

C = π × 12,756.274 k m

C = 40,075.016 k m

We did not select the diameter randomly. To three decimal places, that circumference of the earth’s equator.

How to find the circumference and area of a circle

The Encyclopedia Britannica tells us that a historic Round Table, rumored to be King Arthur’s, has a radius of 2.75 m e t e r s . To find the circumference of the circle that is King Arthur’s table, we use the radius formula:

That is a massive table. Arthur supposedly gathered 25 knights, though, so with all 26 men gathered around, each had only 69 centimeters of table edge to himself. They would have been elbow to elbow, those knights.

You can also find circumference with the area of a circle.

Find Diameter From Circumference

That same equation, C = π d , can also be used to find the diameter of a circle if you know circumference. Just divide both sides by the irrational number π .

Suppose you are told the circle’s circumference is 339.292 f e e t . What is the diameter of the circle?

292 f e e t = π d

No, that diameter is not random; it is the size of the sarsen stone ring at Stonehenge.

How to find the circumference and area of a circle

Find Radius From Circumference

The circumference equation using radius, C = 2 π r , can also be used to find the radius of the circle if you know circumference.

Say we have a circle with a circumference of 40.526 m e t e r s ; what is its radius? We will again divide both sides by π , but we also need to eliminate the 2 , so divide both sides by 2 π :

526 m 2 π = 2 π r 2 π

Of course, that is not a random number. That is the size of Notre Dame Cathedral’s famed South Rose Window. That is a huge big stained glass window!

This lesson has provided you with lots of information the circumference of circles and a way to find any the measure of any one part if you have another measurement. Along the way, you also learned a little geography and history, which may also come in handy to you.

We saw before how to find the perimeter of the polygon. We know that circle is not a polygon. Therefore, it should not have a perimeter. We use an equivalent form for a circle, called circumference.

In this article, we will discuss how to find a circle’s circumference, the circumference of a circle formula, examples, and sample problems about the circumference of a circle.

What is the circumference of a circle?

The distance around a polygon, such as a square or a rectangle, is called the perimeter (P). On the other hand, the distance around a circle is referred to as the circumference (C). Therefore, the circumference of a circle is the linear distance of an edge of the circle.

Why do we do need to calculate the circumference of a circle?

Finding the circumference of an object is important in the following scenarios:

Whether you want to buy a bra, trouser, or sweater, you need to know the distance around your waist or chest. Though your body isn’t a perfect circle, you will have to measure its circumference using a tape measure. Tailors mostly use this technique to determine the circumference of a dress.

You also need to know the circumference of a circle doing craftwork, putting fencing around your hot tub, or just solving a math problem for school.

How to find the circumference of a circle?

As stated before, the perimeter or circumference of a circle is the distance around a circle or any circular shape. The circumference of a circle is the same as the length of a straight line folded or bent to make the circle. The circumference of a circle is measured in meters, kilometers, yards, inches, etc.

There are two ways of finding the perimeter or circumference of a circle. The first formula involves using the radius, and the second involves using the diameter of a circle. It is important to note that both two methods yield the same result.

Let’s take a look.

The circumference of a circle is given by;

C = 2 * π* R = 2πR

How to find the circumference and area of a circle

C = Circumference or perimeter,

R = the radius of a circle,

π = the mathematical constant known as Pi

C = π* D = π D

How to find the circumference and area of a circle

where, D = 2R = The diameter of a circle

For any circle, its circumference ratio to its diameter is equal to a constant known as pi.

C /D = Pi or C/2R = pi

The approximate value of pi (π) = 22/7 = 3.1415926535897…. (a non-terminating value)

For the easier computation of a circle’s circumference, pi’s value is taken to be 3.14 (π = 3.14).

Let’s see a few examples below to polish the concept of the circumference.

Example 1

Find the circumference of the circle with a radius of 8 cm.

Circumference = 2 * π* R = 2πR

Example 2

Calculate the circumference of a circle whose diameter is 70 mm

Circumference = π* D = π D

Example 3

Calculate the perimeter of a circular flower garden whose radius is 10 m.

Circumference = 2 * π* R = 2πR

Example 4

The circumference of a circle is 440 yards. Find the diameter and radius of the circle.

Circumference = 2 * π* R = 2πR

Divide both sides by 6.28 to get,

Therefore, the radius of the circle is 70.06 yards. But, since the diameter is twice the radius of a circle, the diameter is equal to 140.12 yards.

Example 5

The diameter of the wheels of a bicycle is 100 cm. How many revolutions will each wheel make to travel a distance of 157 meters?

Calculate the circumference of the bicycle’s wheel.

Circumference = π D

To get the number of revolutions of the wheel, divide the distance covered by the circumference of the wheel.

We need to convert 157 meters to cm before dividing, so we multiply 157 by 100 to get 15700 cm. Therefore,

Number of revolutions = 15700 cm/314 cm

Example 6

A piece of a wire in the form of a rectangle of length 100 cm and width 50 cm is cut and folded to make a circle. Calculate the circumference and radius of the circle formed.

The circumference of the circle formed = the perimeter of the rectangular wire.

Perimeter of a rectangle = 2(L + W)

Therefore, the circumference of the circle will be 300 cm.

Now calculate its radius.

Circumference = 2 π R

300 cm = 2 * π * R

300 cm = 2 * 3.14 * R

Divide both sides by 6.28.

So, the radius of the circle will be 47.77 cm.

Example 7

The radius of each wheel of a motorcycle is 0. 85 m. How far will the motorcycle move if each wheel takes 1000 revolutions? Assume the motorcycle is moving on a straight line.

First, find the circumference of the wheel.

Circumference = 2 π R

To find the distance traveled, multiply the circumference of the wheel by the number of revolutions taken.

Distance = 5.338 * 1000

Therefore, the distance traveled is equal to 5.338 kilometers.

A circle is a simple closed shape. The mathematical definition of circle is it is a set of all points in a plane which are at a constant given distance (radius) from a given point (center). Explained using conic sections, a circle is a conic section obtained by the intersection of a cone with a plane perpendicular to the cones symmetry axis. Circle is a two- dimensional figure having no edge and no vertex. So as any regular two- dimensional closed figure, it has two main properties i.e. it has a perimeter and an area.

Here we will be looking at how to calculate the perimeter or the circumference of the circle. Lets first look through the basic terminology.

  • Perimeter or circumference is the continuous line forming the boundary of closed geometrical figure
  • Area is the quantity that expresses the extent of a two- dimensional figure or shape in the plane.
  • The center of circle is a point which is equidistant from the points on the edge of the circle.
  • The radius of a circle is the distance from the center point to the point on the circle. Since, circle has radial symmetry, the distance is same of a circle.
  • The straight line passing from one side to the other through the center of the circle is called the diameter.
  • The number pi or ? is a mathematical constant used to calculate the circumference and the area of the circle. Being an irrational number, ? cannot be expressed as an exact numerical form but it is usually generalized as 3.14 or 22/7 for calculation purposes.

Before the formula were created, there were other ways to calculate the circumference of the circle.

For instance, a string was used to go along the continuous boundary of the circle and it was straighten to check the perimeter it covers.

Here, we will talk about three formulas of calculating the circumference of a circle

How to find the circumference and area of a circle

When the radius is given-

The formula used when the radius of a circle is given is:

Here, C is the circumference and r is the radius given.

Lets learn this using an example-

  • Calculate the circumference of circle with radius 14cm

Solution – here, the radius given is, r = 14 cm

  • C=2?r
  • C= 2?14
  • C= 2(22/7)(14) or 2(3.14)(14)
  • C= 88 cm

Hence, the circumference of the circle is 88 cm.

When the diameter is given-

The formula used when the diameter of a circle is given is-

Here, C is the circumference of the circle and d is the given diameter of the circle.

Lets learn this using simple problem-

  • Calculate the circumference of the circle of diameter 14 cm.

Solution- here, diameter given is, d = 14 cm

  • C=?d
  • C=?14
  • C= 22/7(14) or 3.14(14)
  • C= 44 cm

Hence, the circumference of the circle is 44 cm.

When the area of the circle is given-

This formula might look a bit complicated, but it isnt.The formula used when the area of the circle is given is-

Here, C is the circumference of the circle and A is the given area of the circle.

Lets learn this using simple problem-

  • Calculate the circumference of the circle of area 14 cm

Solution- here, area given is, A = 14 cm

  • C= 2 ? ? A
  • C= 2 ? ? (14)
  • C= 2 ? (22/7)(14) or C= 2 ? (3.14)(14)
  • C= 13.26 cm

Hence, the circumference of the circle is 13.26 cm

In these lessons, we will learn

  • the formula for the area of a circle
  • how to find the area of a circle given radius or diameter,
  • how to solve word problems using the area of a circle,
  • when given the area, how to find the radius or diameter,
  • when given the area, how to find the circumference,
  • how to prove the formula for the area of a circle.

We have also added an Area of Circle calculator at the end of this page.

The following diagram gives the formula for the area of a circle. Scroll down the page for more examples and solutions on how to use the formula and also a proof or the formula.

How to find the circumference and area of a circle

Formula for the Area of a Circle

A circle is a closed curve formed by a set of points on a plane that are the same distance from its center. The area of a circle is the region enclosed by the circle. The area of a circle is equals to pi (ПЂ) multiplied by its radius squared.

Pi (ПЂ) is the ratio of the circumference of a circle to its diameter. Pi is always the same number for any circle. The value of ПЂ (pi) is approximately 3.14159265358979323846… but usually rounding to 3.142 should be sufficient.

The area of a circle is given by the formula:

A = ПЂr 2 В В (see a mnemonic for this formula)
where A is the area and r is the radius.

Since the formula is only given in terms of radius, remember to change from diameter to radius when necessary. The radius is equals to half the diameter.

Area of a circle given the diameter or radius

Example 1:
Find the area the circle with a diameter of 10 inches.

Step 1: Write down the formula: A = πr 2
Step 2: Change diameter to radius:
Step 3: Plug in the value: A = π5 2 = 25π

Answer: The area of the circle is 25π ≈ 78.55 square inches.

Example 2:
Find the area the circle with a radius of 10 inches.

Step 1: Write down the formula: A = πr 2
Step 2: Plug in the value: A = π10 2 = 100π

Answer: The area of the circle is 100π ≈ 314.2 square inches.

How to use the formula A = ПЂr 2 to calculate the area of the circle given the radius?

Example:
Find the area of a circle with radius 4cm.

How to use the formula to calculate the area of the circle given the radius or the diameter?

  1. Find the area of a circle with radius 3cm.
  2. Find the area of a circle with diameter 20cm.
  • Show Video Lesson

    Word Problems using area of circles
    The following videos show how to solve word problems using the area of circles.

    Example:
    There are two circles such that the radius of the larger circle is three times the radius of the smaller circle.
    (a) How many times the circumference of the larger circle is the circumference of the smaller circle?
    (b) What is the ratio of the area of the larger circle to the area of the smaller circle?

    Area and Circumference Word Problems
    Example 1: Janell wants to replace the glass in her mirrors. She can buy glass for $0.89 per square inch. If the price includes tax, how much would she pay, to the nearest penny?

    Example 2: The rectangle has a length of 21 inches and each circle is congruent. What is the area of one circle?

    Example 3: A tire from Karen’s car is shown below. What is the closest distance traveled, in feet, after 3 full rotations of the tire?

    Find radius or diameter of a circle when given the area
    From the formula A = ПЂr 2 , we see that we can find the radius of a circle by dividing its area by ПЂ and then get the positive square-root. The diameter is then twice the radius. This video shows how to find the radius or diameter of a circle when given the area.

    Examples:
    The area of a circle is 12.56 yd 2 . What is the circle’s diameter? (take ПЂ = 3.14)

    Find the circumference of a circle, given the area

    To find the circumference of a circle when given the area, we first use the area to find the radius. Then, we use the radius to find the circumference of the circle.

    How to find the circumference of a circle given the area?

    Example:
    The area of the circle is 12.56 cm 2 . What is the circle’s circumference?

    How to calculate areas of circles and also composite shapes with circles or segments of circles?

    The shape is made from 4 semicircles of diameter 8m and a square of side 8m. The radius of each circle is therefore 4m, and you have the equivalent of 2 whole circles. Then add on the area of the square.

    Proof for the formula of a circle

    The following diagram shows a visual proof for the formula of the area of a circle.

    How to find the circumference and area of a circle

    Graphical proof of the formula of a circle
    It involves dividing the circle into many sectors and rearranging the sectors to form a rectangle. The base of the rectangle is shown to be ПЂr and the height of the rectangle is r. The area of the rectangle is then the product of ПЂr and r. The area of the circle which is equal to area of the rectangle is then ПЂr 2 .

    Area of Circle Calculator

    Enter the radius and this area of circle calculator will give you the area. Use it to check your answers.

    Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
    How to find the circumference and area of a circle

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    echo -n “Enter the radius of a circle : “

    # use formula to get it

    area=$ ( echo “scale=2;3.14 * ($r * $r)” | bc )

    # use formula to get it

    d=$ ( echo “scale=2;2 * $r”|bc )

    circumference=$ ( echo “scale=2;3.14 * $d”| bc )

    echo “Area of circle is $area”

    echo “Circumference of circle is $circumference”

    Add your answer:

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    Shell script to find area of a circle?

    echo -n “Enter the radius of a circle : “read r# use formula to get itarea=$(echo “scale=2;3.14 * ($r * $r)” | bc)# use formula to get itd=$(echo “scale=2;2 * $r”|bc)circumference=$(echo “scale=2;3.14 * $d”| bc)echo “Area of circle is $area”echo “Circumference of circle is $circumference”

    How to Calculate Circumference, Diameter, Area, and Radius

    The circle calculator finds the area, radius, diameter and circumference of a circle labeled as a, r, d and c respectively.

    For those having difficulty using formulas manually to find the area, circumference, radius and diameter of a circle, this circle calculator is just for you. The equations will be given below so you can see how the calculator obtains the values, but all you have to do is input the basic information. The calculator does the rest.
    How to find the circumference and area of a circle

    Finding the Circumference:

    The circumference is similar to the perimeter in that it is the total length needed to draw the circle.

    We note the circumference as c.

    This depends on whether or not you know the radius (r) or the diameter (d)

    Let’s calculate one manually, for example.

    If r = 6 cm, the the circumference is c = 2π(6) = 12π cm, if writing in terms of π. If you prefer a numerical value, the answer rounded to the nearest tenth is 37.7 cm.

    Suppose you only know the diameter? If the diameter is 8 cm, then the circumference is c = π(8) = 8π or 25.1 cm, rounded to the nearest tenth.

    A great thing about the formulas is that you can manipulate it to solve for an unknown if you know one of the other quantities. For example, if we know the circumference, but don’t know the radius, you can solve c = 2πr for r and get \(r = \frac<2\pi>\). Similiarly, if you want the diameter from the circumference, simply take c =πd and solve for d to get d = \(\frac<\pi>\).

    Finding the Area:

    Let a = area of the circle

    If you know the diameter and not the radius, simply divide the diameter by 2 to get the radius and still use the formula above.

    Again, the formula can be used to solve for the radius, if you know the area. Simply divide a by π to get r² and take the square root of
    the result.

    If you wish to know the diameter from the area, follow the procedure above but double the result you get for r. This is because the diameter is twice the length of the radius.

    Try an example manually to get the area.

    Suppose r = 5 inches

    If rounding to the nearest tenth the area is 78.5 square inches.

    If you know the diameter, simply divide by 2 to get the radius and use the same formula as above.

    Of course, you don’t have to go through all the manual calculations to use this calculator. Simply input the information you know and the rest will be computed for you nearly instantly.

    First off I would like to state that this is a homework assignment. However, I am not looking for you to complete anything for me. I code I am posting is the completed homework assignment. However, since this is my first time using C++ I was curious if there might have been a better method to accomplish the same task.

    Here is the outcome of all changes I have made to the code above. I was able to solve how to handle an input other than of the the required data type.

    How to find the circumference and area of a circle

    4 Answers 4

    Extremely good for a first time at C++! A few things though:

    • #include should be #include
    • Same with #include
    • Also, no need for the ; after the cmath include
    • main does not have a return type of bool . See this or this.
    • I would put the using declarations after all includes. It should be safe, but no need to pull things into the global namespace until the last minute.
    • cin >> radius; doesn’t check for failure or success (see note below)
    • In your final output, you used all endl and then have a random \n
      • \n and endl are not functionality-wise equivalent. In this situation though, that difference is not going to matter. I suggest you either stick with all endl or have all \n and then a final endl (I would probably use all endl just for the consistency). endl is essentially equivalent to writing a newline and flushing
    • I’m not a fan of system(“pause”);
      • It’s system dependent. (The ‘pause’ part, not the system part.)
      • And, in my opinion, your program has no reason to remain running once it’s done. Leave it up to the user whether or not to leave the prompt open.
      • Additionally, though it seems like system(“pause”); is a quick little solution, it may be better to just block on reading any character if you’re determined to leave the application running. system seems a bit overkill.

    Note about cin >> radius;

    The typical approach with handling istream s is to use the extraction as a bool:

    To be honest, I’m not actually sure what the idiomatic way to force a user to provide a valid input is. Hopefully one of the (much) more knowledge C++ regulars will comment on that. My guess though would be to use ignore() to clear out cin ‘s buffer and try to grab a new input.