Circumference of a Circle Formula

# Circumference of a Circle Formula

## Circumference of a Circle

A circle is a path taken by a point which moves in such a way that its distance from a fixed point, in a plane, is always constant. The fixed point is called the centre and the distance between the moving point and the fixed point is called the radius.

The distance covered to go round a circle once is called circumference.

The ratio of the circumference of a circle and its diameter is always constant.

Let us try to verify the result using the following activity.

Activity: Rim of all the vehicles is circular. Different types of vehicles are parked in the school parking lot such as bicycle, bus, car, scooter and the size of the rim of each vehicle is different. Use a thread to measure the circumference of circular rim of four different types of vehicles. Also, measure the length of the diameter of each rim and tabulate the data as follows:

 Rim (circle) Circumference (c) Diameter (d) c/d Bicycle Bus Car Scooter

Now, find the ratio of the circumference and the diameter for each rim (circle).

You will observe that in each case, the ratio between the circumference and the diameter is always 22/7.

This ratio is known as π (pie).

Thus, we have

Circumference/Diameter = π

Circumference = π × diameter

= π × 2r                  (Diameter = 2 × radius)

Thus, Circumference of a circle = 2πr

Where π ≈ 3.14 or 22/7 approximately.

The constant π is an irrational number. Its approximate value is 22/7. Unless otherwise stated, we shall take the value of π as 22/7.

### Circumference of a Circle Formula

Circumference of a circle = 2πr

Example 1: Find the circumference of a circle with radius 7 cm.

Solution: Here, r = 7 cm

We know that,

Circumference of a circle = 2πr

= 2πr = 2 × 22/7 × 7 cm

= 44 cm

Example 2: Find the circumference of a circle with diameter 21 cm.

Solution: Here, diameter = 14 cm, therefore, r = 21/2 = 10.5 cm

Circumference of a circle = 2πr = 2 × 22/7 × 10.5

= 66 cm

Example 3: A piece of wire, which is in the shape of a rectangle having length of 80

cm and breadth of 52 cm, is reshaped and bent into the form of a circle. Find the

Solution: Given: Length of the rectangle = 80 cm and breadth of the rectangle = 52

cm

Perimeter of the rectangle = 2(80 + 52) cm = 264 cm

Circumference of the circle = 264 cm

r = 264

r = 264/2π

r = 132/π = 132 × 7/22 = 42 cm

Radius of the circle = 42 cm

Example 4: The radius of a wheel of a car is 49 cm. How many revolutions will the

Wheel complete to travel 154 km.

Solution: We have, radius of the wheel of the car = 49 cm

Circumference of the wheel of the car = 2πr = 2 × 22/7 × 49

= 308 cm

Distance travelled by the car in one revolution of the wheel = 308 cm

Total distance covered by the car = 154 km = 154 × 1000 × 100 cm = 15400000 cm

Number of revolutions = 15400000/308 = 50,000

Thus, the wheel will complete 50,000 revolutions to travel 154 km.