IGCSE Mathematics: Mensuration — Practice Questions

These are original questions written for Marlbridge, in the style and at the standard of the examination. They are not reproduced past-paper questions — examination boards hold copyright in their own papers. Use these alongside the official past papers available free from your board.

Related: Mensuration revision notes

---

Questions

1. Convert 3.4 m² into cm². [2]

2. A rectangle has length 9 cm and width 6 cm. Calculate its area and perimeter. [2]

3. A circle has radius 8 cm. Taking π = 3.142, calculate:

(a) the circumference of the circle. [2] (b) the area of the circle. [2]

4. A sector of a circle has radius 8 cm and a sector angle of 60°. Taking π = 3.142, calculate:

(a) the arc length of the sector. [2] (b) the area of the sector. [2]

5. A cylinder has radius 4 cm and height 10 cm. Taking π = 3.142, calculate:

(a) its volume. [2] (b) its total surface area. [3]

6. A cone has radius 3 cm and slant height 5 cm. Taking π = 3.142, calculate:

(a) the perpendicular height of the cone. [2] (b) the volume of the cone. [2]

7. A shape is made from a 10 cm × 6 cm rectangle with a semicircle of diameter 6 cm removed from one short side. Taking π = 3.142, calculate the area of the remaining compound shape. [3]

8. A sphere has radius 6 cm. Taking π = 3.142, calculate its volume, correct to 3 significant figures. [2]

9. A sphere has surface area 314.2 cm². Taking π = 3.142, find its radius. [3]

---

Answers

1. 1 m² = 10 000 cm² [1], so 3.4 m² = 3.4 × 10 000 = 34 000 cm² [1].

2. Area = 9 × 6 = 54 cm² [1]. Perimeter = 2(9 + 6) = 30 cm [1].

3. (a) C = 2πr = 2 × 3.142 × 8 = 50.3 cm (3 s.f.) [2]. (b) A = πr² = 3.142 × 8² = 201 cm² (3 s.f.) [2].

4. (a) Arc length = (60/360) × 2 × 3.142 × 8 = (1/6) × 50.27 [1] = 8.38 cm (3 s.f.) [1]. (b) Sector area = (60/360) × 3.142 × 8² = (1/6) × 201.1 [1] = 33.5 cm² (3 s.f.) [1].

5. (a) V = πr²h = 3.142 × 4² × 10 [1] = 503 cm³ (3 s.f.) [1]. (b) SA = 2πrh + 2πr² = (2 × 3.142 × 4 × 10) + (2 × 3.142 × 4²) [1] = 251.4 + 100.5 [1] = 352 cm² (3 s.f.) [1].

6. (a) Using Pythagoras: h² = 5² − 3² = 25 − 9 = 16 [1] → h = 4 cm [1]. (b) V = ⅓πr²h = ⅓ × 3.142 × 3² × 4 [1] = 37.7 cm³ (3 s.f.) [1].

7. Rectangle area = 10 × 6 = 60 cm² [1]. Semicircle radius = 3 cm, area = ½ × 3.142 × 3² = 14.14 cm² [1]. Remaining area = 60 − 14.14 = 45.9 cm² (3 s.f.) [1].

8. V = (4/3)πr³ = (4/3) × 3.142 × 6³ [1] = (4/3) × 3.142 × 216 = 905 cm³ (3 s.f.) [1].

9. SA = 4πr² → r² = 314.2 ÷ (4 × 3.142) [1] = 314.2 ÷ 12.568 = 25 [1] → r = √25 = 5 cm [1].

---

Where marks are usually lost

• Converting between area units by the linear conversion factor instead of squaring it (1 m² is 10 000 cm², not 100 cm²).
• Forgetting the fraction of a full turn (angle ÷ 360) when finding an arc length or sector area.
• Mixing up the formulas for curved surface area and total surface area of a cylinder or cone — total surface area needs the circular end(s) added on.
• Using the slant height instead of the perpendicular height in the volume formula for a cone (they are different lengths, related by Pythagoras).
• Adding areas instead of subtracting when a compound shape has a piece removed, or the reverse.
• Not rounding to 3 significant figures (or as instructed) only at the final answer, and rounding too early in a multi-step calculation.

Examiner report insight

• For a major sector or arc, first find the correct (larger) angle by subtracting the given angle from 360 degrees – applying the fraction-of-360 formula directly to the given (minor) angle answers the wrong region.
• Mixing up the radius and the diameter partway through a multi-step compound-shape or composite-solid calculation – write down which one the question actually gave before substituting.
• Finding a linear scale factor from a volume ratio requires a cube root, not a square root – the square root gives a linear scale factor from an area ratio instead.

Source: Cambridge International, 0580 Mathematics Principal Examiner Report, June 2024 series, Papers 11, 13, 21 (verified 2026-09-02).

Approaching mensuration questions

The most reliable way to avoid unit and formula errors on this topic is to write down which formula the question needs before substituting any numbers, and to check the given units against what the answer needs to be in – since a wrong unit conversion or a swapped slant/perpendicular height produces an answer that still looks numerically plausible, it will not stand out as obviously wrong the way an arithmetic slip often does. For compound shapes, sketch (or describe to yourself) exactly which simple shapes the compound shape is built from and whether each one is added or removed, before calculating any individual area or volume.