4024/12 May/Jun 2026, Question 19: Surface Area of a Cuboid and Cylinder
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 6 marks
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The question, in short
A hemisphere of radius 3x and a cylinder of radius 2x and height kx have equal volumes. Find the cylinder's total surface area in the form aπx².
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Solution · 6 marks
- 1Hemisphere volume = 1/2 × 4/3 π(3x)³ = 18πx³
- 2Cylinder volume = π(2x)² × kx = 4kπx³
- 34k = 18, so k = 9/2 and height = 9/2 x
- 4Surface area = 2 × π(2x)² + 2π × 2x × 9/2 x
- 5= 8πx² + 18πx² = 26πx²
Answer26πx²
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