The circumference is the distance around a circle.

Measure the diameter of the circle.

Place a piece of string round the circle and then open it out flat:

Measure the length of the line:

What is the connection between the diameter and the circumference?

diameter

Measure the distance around the outside of each circle. Measure the diameter of each circle and complete the table.

Circle Circumference Diameter

A

B

C

D

Circle A

Circle B

Circle C

Circle D

The circumference is the distance around a circle.

diameter1 2 3 0.1

circumference

Circumference is equal to roughly 3 x diameter…….and this works or every

circle!

It’s not easy to use a ruler to measure the distance around a circle.

A formula for the circumference makes finding it easy.

The symbol, , (pi) is said as pie, and is 3.14 (to 2 dp). This is how accurate we need to be on the GCSE calculator paper.

A formula for the connection between the circumference and the diameter is

C dd

Find the circumference of the circle below:

C d

3.14 10C

31.4 cmC

How to find circumference given the diameter of a circle

If you have the diameter: multiply the diameter by 3.14 ().

State the formula

Substitute the values for and d.

10 cm

Questions: Given diameter, find the circumference

Find the circumference of the circle below:

C d

3.14 6C 18.84 mC

How to find circumference given the radius

If you have the radius: multiply this by 2 first to get the diameter.

State the formula

Substitute the values for and d.

Then multiply the diameter by 3.14 ().

3 m

2 3 6d

Questions:Given radius, calculate the circumference

Review

Answers

A B C D E F

r = 3 cmr = 5 cmd = 3 cmr = 7 cmd = 4 cmd = 2.5 cm

1 2 3 4 5 6

12.6 18.8 9.4 7.9 31.4 44.0cm cm cm cm cm cm

6 10 3 14 4 2.518.84955592 31.41592654 9.424777961 43.98229715 12.56637061 7.853981634

A2 B5 C3 D6 E1 F4

Calculate the missing numbers in the table below using the circumference formula below.

What’s the formula?

13.502

6.8

5

C (cm) d (cm) r (cm)

C dUse 3.14 as an approximation for .

10

3.4

31.4

21.352

4.3 2.15

Plenary• You should know the words used in a circle to include the diameter, radius, circumference and .

• Know and use the formula for the circumference of a circle.

• Know that is roughly 3.14.

C d 2C ror

Find the circumference of each circle below.

8 cm12 cm

C dC d

2 8 16d

3.14 16C

50.24 cmC

3.14 12C

37.68 cmC