4024/12 Oct/Nov 2025, Question 18: Volume and Surface Area of a Sphere
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 5 marks
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The question, in short
Cylinder and hemisphere share equal radius and equal volume; cylinder height is 6 cm. Find the hemisphere's total surface area in terms of π.
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Solution · 5 marks
- 1Volume of cylinder = πr² × 6, volume of hemisphere = 1/2 × 4/3 × πr³ = 2/3 πr³
- 26πr² = 2/3 πr³
- 3r = 6 × 3/2 = 9 cm
- 4Total surface area = curved surface + flat circle = 1/2 × 4π × 9² + π × 9²
- 5= 162π + 81π = 243π cm²
Answer243π
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