The idea, step by step
Three different lengths
The radius joins the centre to a point on the circle. A diameter passes through the centre and reaches the circle at both ends, so its length is twice the radius. Circumference is the entire curved boundary. It is a perimeter, not an area.
Why pi appears
For every circle, circumference divided by diameter is the same number, called pi. Pi is irrational, so its decimal continues without repeating. Use the symbol π for an exact answer, or the approximation requested. For hand calculations, a question may supply π ≈ 3.14. Do not round partway through a multi-step calculation.
A common trap
Treating a radius label as if it were the diameter.
Instead: Check the endpoints of the marked segment. If it starts at the centre, double it before using C = πd.
See the thinking
Radius supplied
A circle has radius 5 cm. Find its circumference exactly.
- Diameter = 2 × 5 = 10 cm.
- Circumference = π × 10.
Working backwards
A circle has circumference 18π cm. Find its radius.
- C = πd, so d = 18 cm.
- Radius is half the diameter: 18 ÷ 2 = 9 cm.
Check your understanding
A circle has diameter 14 cm. Give its radius and exact circumference.
Show answer
and
Radius = 14 ÷ 2; circumference = π × 14.
Your turn
6 questions · 11 marks · Work at your own pace.
Read the questions online
- A circle has radius 7 cm. Find its diameter.1 mark
- A circle has diameter 9 m. Find its radius.1 mark
- Find the exact circumference of a circle of radius 4 cm.2 marks
- A wheel has diameter 20 cm. Using π ≈ 3.14, find the distance travelled in one complete turn without slipping.2 marks
- A circle has circumference 24π cm. Find its diameter and radius.2 marks
- A semicircle has diameter 10 cm. Find its complete perimeter, including the straight edge, exactly.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A circle has radius 7 cm. Find its diameter.1 mark
2 × 7 = 14 cm.
14 cm - A circle has diameter 9 m. Find its radius.1 mark
9 ÷ 2 = 4.5 m.
4.5 m - Find the exact circumference of a circle of radius 4 cm.2 marks
Diameter = 8 cm.
C = π × 8.
- A wheel has diameter 20 cm. Using π ≈ 3.14, find the distance travelled in one complete turn without slipping.2 marks
One turn travels one circumference.
3.14 × 20 = 62.8 cm.
62.8 cm - A circle has circumference 24π cm. Find its diameter and radius.2 marks
Divide C by π to find d = 24 cm.
Halve the diameter to find r = 12 cm.
Diameter 24 cm; radius 12 cm - A semicircle has diameter 10 cm. Find its complete perimeter, including the straight edge, exactly.3 marks
Full circumference would be 10π cm.
The curved half is 5π cm.
Add the straight diameter of 10 cm.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Year 7 measurement and spatial representation: areas of triangles/parallelograms, prism volumes, circle circumference, nets and views. Precision is integrated into practical measurement; circle area is not introduced here.
Official curriculum source ↗