Perimeter of Circle

A circle is the locus of points that are equidistant from a given point. If we take any point in the plane and connect all the points in the plane that are at a given distance say 2 cm or 5 cm from the point, we will get a circle.

The fixed point is the centre of the circle and the given distance is called the radius of the circle. The  distance between a pair of points on the circle that are farthest apart is called the diameter of the circle and is twice the measure of the radius. If we connect such pair of points with a line segment, it will always pass through the centre of the circle.

The perimeter of a circle is the length as measured along the boundary lines of the circle. The perimeter is also called circumference.

How to find the Perimeter of a circle

Before we proceed to learn how to find the perimeter of a circle, let us understand the concept of perimeter of a circle with an example.

Imagine that we have to travel along a thin perfect circular road in an automobile. Let us assume that we are starting from a point A on the circle. Note down the odometer reading of the automobile at the start of the journey. Start the vehicle and travel along the boundary of the circle and come back to the same point A without deviating from the boundary. Note down the odometer reading again. The difference between the two odometer readings give the distance traveled along the circle and this is the perimeter of the circle

Since perimeter is a measure of distance, it has the same units as that of distance like millimetre (mm), centimeter (cm), metre (m) etc

There is a simple formula to calculate the perimeter of a circle once we know the radius of the circle. The formula for the perimeter of a circle is given by

C = 2 x  `pi`   x r

C= Circumference of the circle or the Perimeter of the circle

`pi` = Pi,  the value of `pi ` is approximately taken as 3.14

r= radius of the circle

But diameter of the circle is twice the radius

diameter = 2 x radius

The formula for the perimeter of a circle  can also be written as

C= `pi` x  d

Where d = diameter

The value of `pi`  is constant and assumed to 3.14.  For the time being `pi `can be understood as a constant obtained when the circumference of any circle is divided by its diameter. In higher mathematics, you will learn about more advanced definitions for `pi `and also how to derive the value of `pi `accurately.

Let us work out simple examples on how to find the perimeter of  a circle

Ex 1 : The radius of circle is 5 cm what is the circumference?

Sol : C= 2 x `pi` x r

Step 1: C= 2 x 3.14 x 5

Step 2:  C = 31.4 m

Note : Your answers should always have the units mentioned clearly else it is incomplete.

Ex. 2:  The wheel of a bullock cart has a radius of 3 m. If the wheel rotates once how much distance does the cart move?

Sol: When the wheel rotates once, the cart will move by a distance equal to the perimeter of the wheel.

Step 1: C= 2 x `pi`  x r

Step 2: C= 2 x 3.14 x 3 = 18.84 m

The bullock cart moves 18.84 m in one revolution of the wheel

Exercises on Perimeter of a circle

Let us summarize how to find the perimeter of  a circle. The perimeter of a circle can be obtained form the formula

Perimeter of the circle = 2 x `pi`  x radius of the circle or `pi`  x diameter of the circle

Pro 1: A cart wheel has a diameter of 1m. How many times should the wheels roll for the cart to travel 1 km?

Ans: 318.47 revolutions

Pro 2: The wheel of an automobile has a diameter of 2m and rotates 40 times in a minute, What is the speed of the automobile?

Ans: 15.072 Kmph

Algebra is widely used in day to day activities watch out for my forthcoming posts on evaluating an algebraic expression and cbse syllabus for class 10. I am sure they will be helpful.

Hint: Find the distance traveled in 40 rotations which is perimeter multiplied by 40. Calculate speed as distance traveled divided by time.

Pro 3: The circular coin of diameter 2 cm rolls 6.28 cm along the ground in one revolution. Can you calculate the value of `pi`  from the given data ?

Ans 3.14