O Level Mathematics: Mensuration Practice Questions (Cambridge 4024)

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs — Cambridge International holds copyright in its own papers. Use these alongside the official past papers available from your board.

Most questions practise a skill tested in the June 2025 papers. Questions marked (no calculator) are Paper 1 style; the rest allow a calculator, as in Paper 2. After each answer there is a tip and the real question to try next.

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Questions

1. Convert 3.2 m² to cm². [1]

2. (no calculator) A sector of a circle has radius 9 cm and arc length 5π cm. Find the angle of the sector and its area, giving the area in terms of π. [3]

3. (no calculator) A circle has area 36π cm². Find its circumference in terms of π. [2]

4. (no calculator) A cylinder has radius 5 cm and height 8 cm. Find its volume in terms of π. [2]

5. A solid is made by joining a cone to a hemisphere. Both have diameter 12 cm. The total height of the solid is 20 cm. Find the volume of the solid. [4]

6. A trapezium has parallel sides of 7 cm and 11 cm, and a perpendicular height of 5 cm. Find its area. [2]

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Answers

1. 1 m² = 100 × 100 = 10 000 cm², so 3.2 m² = 32 000 cm² [1].

Tip: square the length conversion: there are 100² square centimetres in a square metre.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 22, Question 5.

2. 5π = (θ/360) × 2π × 9, so θ = 100° [1]. Area = (100/360) × π × 9² [1] = 22.5π cm² [1].

Tip: find the angle from the arc length first, then use it for the area.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 12, Question 23.

3. πr² = 36π, so r = 6 cm [1]. Circumference = 2π × 6 = 12π cm [1].

Tip: work back to the radius before using any other formula.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 12, Question 23.

4. V = π × 5² × 8 [1] = 200π cm³ [1].

Tip: square the radius, not the diameter.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 22, Question 21.

5. Radius = 6 cm, so the height of the cone = 20 − 6 = 14 cm [1]. Hemisphere = ⅔π × 6³ = 144π [1]. Cone = ⅓π × 6² × 14 = 168π [1]. Total = 312π = 980 cm³ (3 s.f.) [1].

Tip: the hemisphere’s height is its radius; subtract it from the total height to get the cone’s height.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 22, Question 21.

6. ½ × (7 + 11) × 5 [1] = 45 cm² [1].

Tip: the height must be perpendicular to the parallel sides.

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Where marks are usually lost

• Converting m² to cm² by multiplying by 100 instead of 10 000.
• Using the diameter as the radius.
• Using the total height of a composite solid as the cone’s height.