0580/23 Oct/Nov 2025, Question 29: Surface Area of a Cuboid and Cylinder
Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 5 marks
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The question, in short
Given solid A (cylinder height 5R with hemisphere, radius 2R) and cone B (radius R, sloping edge x) with equal total surface areas, find R in terms of x.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1Solid A: base = π(2R)² = 4πR², curved cylinder = 2 × π × 2R × 5R = 20πR², hemisphere = 4π(2R)²/2 = 8πR²
- 2Total A = 4πR² + 20πR² + 8πR² = 32πR²
- 3Solid B: πRx + πR²
- 432πR² = πRx + πR², so 31R² = Rx
- 5R = x/31
Answerx/31
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