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Mensuration: surface area of solids — KCSE Mathematics

KCSE Mathematics · 95 practice questions · 3 syllabus objectives

33 easy35 medium27 hard

What You'll Learn

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

Calculate the total surface area of a cuboid, cylinder, cone and sphere

Calculate the surface area of composite solids formed by combining two or more basic shapes

Mensuration: surface area of solids

Sample Questions

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1
easySHORT ANSWER4 marks

A cone has a base radius of 4 cm and a height of 6 cm. Determine its total surface area. (Use π = 22/7) (4 marks)

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Part (a) — 4 marks
Calculate the slant height using Pythagoras' theorem: l = √(r² + h²) (1 mk)
Curved surface area = πrl = 22/7 × 4 × l (1 mk)
Area of circular base = πr² = 22/7 × 4² (1 mk)
Total surface area = Curved surface area + Area of circular base (1 mk)
2
easySHORT ANSWER3 marks

A cylindrical storage tank has a radius of 3 m and a height of 5 m. Calculate its total surface area. (Take π = 3.142) (3 marks)

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Part (a) — 3 marks
Curved surface area = 2πrh = 2 × 3.142 × 3 × 5 (1 mk)
Area of circular top and bottom = 2 × πr² = 2 × 3.142 × 3² (1 mk)
Total surface area = Curved surface area + Area of circular top and bottom (1 mk)
3
easySHORT ANSWER4 marks

A cylinder has a radius of 4 cm and a height of 10 cm. Calculate its total surface area. (4 marks)

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Part (a) — 4 marks
Total surface area = 2πr(h + r) (1 mk)
Substituting values: = 2 * 22/7 * 4 * (10 + 4) (1 mk)
Calculate the height and radius: = 2 * 22/7 * 4 * 14 (1 mk)
Final calculation = 2 * 22/7 * 56 = 704/7 ≈ 100.57 cm² (1 mk)
4

Calculate the total surface area of a cuboid with a length of 10 cm, a width of 5 cm, and a height of 3 cm. (3 marks)

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