How to Find the Perimeter or Circumference of a Circle & Formula


How to find the circumference of a circle or perimeter of a circle? It’s a common question for all of us, especially all school-going children. In this article, we will discuss the very basic principle about the circumference of a circle.

A lot of diagrams along with examples, exercises are explained to understand the basic concept.

Let’s explore, the concept!

How to Find the Circumference of a Circle

We will see here, how to find the circumference of a circle. In our many mathematical calculations, we use the term perimeter of a circle and do our calculations. Now, this perimeter is required to be known as,

  • It is required for the area calculation of a circle or cylinder.
  • The length of the circle can be calculated.
  • The length by which a circle can be made.

Let’s get into the main article!

Perimeter of a Circle Terminology

Before understanding what is the circumference of a circle, we will learn a few terminologies related to a circle,

  • Circle
  • Center
  • Circumference or perimeter of a circle
  • Radius
  • Diameter
circumference of a circle perimeter terminology
Circumference of a circle perimeter terminology

Circle

The circle is one type of shape in geometry where the distance between the edge of the circle to the center is the same at any point.

Centre

It is basically the centre of the circle.

Circumference 

We have already learned that perimeter means the distance or the length of the surrounding area and we have already calculated the perimeter of square. In the case of circle, the term normally used circumference.

Radius

Radius is the distance from the edge of the circle to the center. It is denoted as ‘r’.

Diameter 

Diameter is the length of any straight line in a circle that passes through the center.

  • It is twice the radius that means ‘2r’.
  • Diameter is denoted as ‘d’.
  • So, we can write, d=2r.

Semi-circle 

Semi-circle means half of the circle. If the diameter splits the circle into two halves, each part will be called a semi-circle.

Pi value

  • Pi is a constant which is equal to the ratio of circumference and diameter.
  • The value of Pi is 22/7 or 3.141592….. or 3.14 approximately.
  • It is unitless.
  • It is denoted as a Greek letter ‘π’.

Circumference of a Circle

Circumference of a circle means the perimeter of the circle basically. It is the same philosophy like squares or rectangles. Now,  in the case of a circle, there is no straight line.

Here, the term circumference comes into the picture. It is simply the distance around a circle or the total length around the circle.

  • Basically total length of any two-dimensional circular surface.
  • It is also called a perimeter of a circle.
  • It is donated as C.
  • In the case of circumference of a semicircle, we normally use ‘c‘.
  • The philosophy is the same as the perimeter of squares or rectangles.

Formula for Circumference of a Circle

In our earlier lesson, we have understood that perimeter implies the total length of the edge. Let’s learn circumference of a circle formula!

Let’s consider,

  • r = Radius of the circle
  • D = Diameter
  • C = Circumference of a circle
  • π = 3.14

So,

C = πD

Perimeter or circumference of a circle = π x Diameter of circle

Or C =  π x 2r = 2πr

circumference of a circle formula
Circumference of a circle formula

Circumference of a circle = 2π x Radius of circle

This is the equation for circumference of a circle.

Now, the circumference of a circle formula is applicable in three ways,

  1. If Radius (r) is known
  2. If Diameter (D) is known
  3. If the Area is known

If Radius (r) is Known 

We can calculate the circumference of a circle if the radius is known,

Circumference or Perimeter (C) = 2 π r

If Diameter (D) is Known

We can calculate the circumference of a circle if the diameter is known,

Circumference or Perimeter (C) = πD

If the Area is Known  

The area of a circle,

A = πD2/4

or, D2 = 4A/π

or, D = √(4A/π)

Circumference,

C = πD

or, C = πD = π√(4A/π) = √(4πA)

These are the circumference of a circle formula.

Perimeter of a Semicircle

We have already found out the perimeter of a circle.

C = 2πr.

Now, for semicircle means half of a circle.

So, the perimeter of a circle = 2πr / 2 = πr

How to find the perimeter of a circle of radius 50m?

We will try to understand the concept of the perimeter of a circle with a simple example step by step.

The circle radius is 50m. Now, what is the perimeter of a circle?

Step-1: Given data is circle radius, r = 50m.

Step-2: Diameter of the circle, D = 2r = 2 x 50m = 100m.

Step-3: Perimeter or circumference, C = πD = 3.14 x 100 m = 314m.

Step-4: It can be directly calculate with using circumference of a circle formula, C = 2πr = 2 x 3.14 x 50 = 314m

Check out the online calculator for the circumference.

Examples of Circumference of a circle

Let us work out a few examples, of how to find out the perimeter of a circle!

Example-1

Take a circular disc. The radius of the circular disc is 5 m. Find out the circumference of the circle.

Solution

Circular disc radius = 5m.

Therefore, the circumference of the circle,

C = 2πr

⇒ C = 2 x 3.14 x 5 m

⇒ C = 31.4 m

Hence, the circumference of the disc is equal to 31.4m.

Example-2

The wheel of a Toyota car has a diameter of 18 inches. Find out the distance covered by the wheel with one rotation.

Solution

Toyota car wheel diameter = D = 18

The perimeter of the wheel = πD = 3.14 x 18 = 56.52 inches.

Hence, the perimeter or the circumference of the wheel is equal to 56.52m.

Example-3

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

Solution

Radius of the perfect circle = 8cm.

Therefore, the circumference of the perfect circle,

C = 2πr

⇒ C = 2 x 3.14 x 8 cm

⇒ C = 50.24 cm

Hence, the perimeter of circle is equal to 50.24cm.

Example-4

Find the diameter of a circle, whose circumference is 66m. [Consider π = 22/7]

Solution

Given data, circumference, C = 49m,

As per equation, we know,

C = πD

⇒ 66 = 22/7 x D

⇒ D = 66 x 7 / 22

⇒ D = 21m.

The perimeter of circle is equal to 21m.

Example-5

The perimeter of a semi-circular scale is 88 cm, find out the radius of the scale. [Consider π = 22/7]

Solution

Given data, perimeter of the semicircle,

c = C/2 = 88cm,

⇒ C = 88×2

As per equation, we can write,

C = 2πr

⇒ 88 x 2 = 2 x 22/7 x r

⇒ r = 88 x 2 x (7 / 22) / 2

⇒ r = 28m.

The perimeter of the semicircle is equal to 28m.

Example-6

The circumference of a circular plate exceeds the radius by 22.7 cm. Find the diameter of the circle. [Consider π = 22/7]
Solution

Since the radius is not give, consider the radius of the circular plate is r cm.

So, based on the definition of the diameter,

We can write,
Diameter, D = 2r

Circumference. C = πD = 2πr cm

Now, as per the condition,

Circular plate exceeds the radius by 22.7 cm
So, Circumference = radius + 22.7
⇒ 2πr = r + 22.7
⇒ 2 × (22 / 7) × r = r + 22.7
⇒ 44r = 7r + 22.7 × 7
⇒ 44r – 7r = 158.9

⇒37 r = 158.9
⇒ r = 158.9 / 37

⇒ r = 4.29
Hence, radius of the circular plate is 4.29cm.

And the diameter, D = 2r = 2 x 4.29 = 8.59cm.

Example-7

Find the circumference of the earth. [Diameter of the earth is 2742km]

Solution

Diameter of the earth, D = 12742km.

Therefore, the circumference of the earth,

C = πD

⇒ C = 3.14 x 12742

⇒ C = 40009.88km

Hence, the circumference of the earth is equal to 40009.88km.

Conclusion

So, we have learned how to find the perimeter of a square and any doubt, please let us know.

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