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Mensuration: volume of solids — KCSE Mathematics

KCSE Mathematics · 107 practice questions · 4 syllabus objectives

37 easy35 medium35 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Calculate the volume of prisms (cuboid, triangular prism, cylinder) using V = cross-sectional area × length

Calculate the volume of pyramids, cones and spheres; find the volume of composite solids

Solve problems involving capacity (converting between cm³, litres, m³) and density (mass = density × volume)

Mensuration: volume of solids

Sample Questions

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1
easySHORT ANSWER3 marks

A fish tank has a length of 1.5 m, a width of 0.5 m, and a height of 0.6 m. If the tank is filled with water, calculate the volume of water in litres. (3 marks)

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Part (a) — 1 mark
Total volume = 1.5 × 0.5 × 0.6 m³ (1 mk)
Part (b) — 1 mark
Convert to litres: 1 m³ = 1000 L, hence volume in litres = total volume × 1000 (1 mk)
Part (c) — 1 mark
Final volume = 450 L (1 mk)
2
easySHORT ANSWER3 marks

A cone has a base radius of 3 cm and a height of 4 cm. Calculate the volume of the cone. (3 marks)

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Part (a) — 3 marks
Volume of cone = ⅓ × π × (3 cm)² × (4 cm) (1 mk)
Volume = ⅓ × π × 9 cm² × 4 cm (1 mk)
Volume = 12π cm³, approximate value is 37.68 cm³ (1 mk)
3
easySHORT ANSWER3 marks

A cylinder has a radius of 3 cm and a height of 5 cm. Find its volume. Use π = 3.14. (3 marks)

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Part (a) — 3 marks
Volume = π × r² × h (1 mk)
Volume = 3.14 × (3 cm)² × 5 cm (1 mk)
Volume = 3.14 × 9 cm² × 5 cm = 141.3 cm³ (1 mk)
4

A triangular prism has a base area of 12 cm² and a height of 10 cm. Calculate the volume of the prism. (2 marks)

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Why Practise Mensuration: volume of solids?

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