The document discusses the circumference of circles. It defines circumference as the distance around a circle and diameter as the distance across a circle. It presents the formula for circumference which is C=πd, where C is circumference, d is diameter, and π is approximately 3.14. Several examples are given of using the formula to calculate the circumference given the diameter. The document also discusses using the alternative radius-based formula, C=2πr, to find circumference when given the radius instead of the diameter.

1. 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

2. 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

3. Circle A
Circle B
Circl
e C
Circle D

4. The circumference is the distance around a
circle.
diameter
1 2 3 0.1
circumference

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

6. 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, π, (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 dπ=
d

7. Find the circumference of the circle below:
C dπ=
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 (π).
State the formula
Substitute the values for π
and d.
10 cm

8. Questions: Given diameter, find the
circumference

9. Find the circumference of the circle below:
C dπ=
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 π
and d.
Then multiply the diameter by
3.14 (π).
3 m
2 3 6d = × =

10. Questions:Given radius, calculate the
circumference

11. Review

12. Answers
A B C D E F
r = 3 cm r = 5 cm d = 3 cm r = 7 cm d = 4 cm d = 2.5 cm
1 2 3 4 5 6
12.6 18.8 9.4 7.9 31.4 44.0
cm cm cm cm cm cm
6 10 3 14 4 2.5
18.84955592 31.41592654 9.424777961 43.98229715 12.56637061 7.853981634
A2 B5 C3 D6 E1 F4

13. 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 dπ=
Use 3.14 as an approximation for π.
10
3.4
31.4
21.352
4.32.15

14. Plenary
• You should know the words used in a circle
to include the diameter, radius,
circumference and π.
• Know and use the formula for the
circumference of a circle.
• Know that π is roughly 3.14.
C dπ= 2C rπ=or

15. Find the circumference of each circle below.
8 cm
12 cm
C dπ=C dπ=
2 8 16d = × =
3.14 16C = ×
50.24 cmC =
3.14 12C = ×
37.68 cmC =