GCSE MATHS PRACTICE

GCSE Area and Circumference of Circles Questions

The radius runs from the centre to the circle's edge; the diameter runs across the circle through its centre and equals twice the radius. Circumference is the distance around the edge: C = 2πr = πd. Area is the space inside: A = πr². Use lengths for circumference and square units for area. Leave answers in terms of π unless another accuracy is requested.

Updated 11 October 2026

Worked example

A circle has diameter 10 cm. Find its circumference and area in terms of π.

Use the labelled measurement; the diagram is not drawn to scale.

The diameter is 10 cm, so the radius is 10 ÷ 2 = 5 cm.
Circumference: C = πd = 10π cm.
Area: A = πr² = π × 5² = 25π cm². Circumference is a length; area uses square units.

Answer: Circumference 10π cm; area 25π cm²

Practice questions

1
Find the circumference of a circle with radius 7 cm. Give your answer in terms of π.
Use the labelled measurement; the diagram is not drawn to scale.
Enlarged diagram
100%Scroll to inspect when enlarged.
2
Find the area of a circle with diameter 12 m. Give your answer in terms of π.
Use the labelled measurement; the diagram is not drawn to scale.
Enlarged diagram
100%Scroll to inspect when enlarged.
3
A circle has circumference 18π cm. Find its radius.
4
A circular pond has radius 4 m. A path 1 m wide surrounds it. Find the area of the path in terms of π.

Show answers

1. 14π cm
2. 36π m²
3. 9 cm
4. 9π m²

Common mistakes

Using diameter in the area formula — Halve the diameter before calculating πr².
Squaring πr instead of r — In πr², square the radius and then multiply by π.
Mixing perimeter and area — Circumference uses cm or m; area uses cm² or m².

More Maths Unlocked lessons

Circumference of a Circle

Opening Maths Unlocked

Preparing the next page…

GCSE Area and Circumference of Circles Questions

Updated 11 October 2026

Worked example

A circle has diameter 10 cm. Find its circumference and area in terms of π.

Use the labelled measurement; the diagram is not drawn to scale.

The diameter is 10 cm, so the radius is 10 ÷ 2 = 5 cm.

Circumference: C = πd = 10π cm.

Area: A = πr² = π × 5² = 25π cm². Circumference is a length; area uses square units.

Answer: Circumference 10π cm; area 25π cm²

Practice questions

Find the circumference of a circle with radius 7 cm. Give your answer in terms of π.

Use the labelled measurement; the diagram is not drawn to scale.

Find the area of a circle with diameter 12 m. Give your answer in terms of π.

Use the labelled measurement; the diagram is not drawn to scale.

A circle has circumference 18π cm. Find its radius.

A circular pond has radius 4 m. A path 1 m wide surrounds it. Find the area of the path in terms of π.

Show answers

1. 14π cm
2. 36π m²
3. 9 cm
4. 9π m²

GCSE Area and Circumference of Circles Questions

Worked example

Practice questions

Common mistakes

Related resources

More Maths Unlocked lessons

GCSE Area and Circumference of Circles Questions

Worked example

Practice questions

Common mistakes

Related resources

More Maths Unlocked lessons