Find the Circumference of a Circle

In this activity, we will find the circumference of a circle

 

You will need a calculator for this!

 

In 250 BC Archimedes used the wheel on a cart to work out that the circumference of any circle is just over 3 times longer than its diameter. 

 

 

Actually 3.14 times longer, or pi times longer.

 

You can try it yourself!

 

You need some string, a ruler and a tin from the cupboard.

1) Wrap the string around the outside of the tin and hold the two ends at exactly the circumference.

2) Put the string along your ruler and measure from end to end of your length - write down the circumference you got.

3) Do the same with the diameter of the tin and write down the length.

4) Divide the circumference by the diameter measurement and it should = 3.14 or just over 3 because we may need a little room for human error here. 

 

 

How does this help though?

 

Well, it means that if we are given the diameter of any circle we can work out the circumference!

 

We use the Greek letter pi (π) to represent the number of times the circumference is longer than the diameter.

Pi is an infinite number, and you can use (π) on your calculator to input the number.

It starts like this 3.14159265359... and goes on and on for ever.

 

In short the formula is:-

 

Circumference = π x diameter

C = π d

 

As the radius is half of the diameter we can also use:-

Circumference = π x 2 x radius

C = 2 π r

 

Write these down because we will use them for the exercise!

 

 

Let's try a question.

 

Example

Find the circumference of a circle with a diameter of 5 cm.

Give your answer to 1 decimal place.

 

Answer

Write the formula first.

Circumference  = π x diameter 

=  π × 5  

 

(Use your calculator button π)

=  15.70796...........

 

We need to give our answer to 1 decimal place

= 15.7 cm

 

Remember, in this activity, you need to use a scientific calculator to calculate pi correctly, you can access one of these online.