0580/22 Oct/Nov 2024, Question 19: Composite Perimeter, Area and Volume
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 7 marks
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The question, in short
For a solid formed by a cylinder of length 11.9 cm and a hemisphere, both with radius 4.3 cm, work out its volume and its total surface area.
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Part (a) · 3 marks
Work out the volume of the whole solid, using the sphere volume formula V = 4/3 πr³ where needed.
- 1Hemisphere = 1/2 × 4/3 × π × 4.3³ = 166.5…
- 2Cylinder = π × 4.3² × 11.9 = 691.2…
- 3Volume = 166.5… + 691.2… = 857.7… ≈ 858 cm³
Answer858 or 857.7 to 857.9
Part (b) · 4 marks
Work out the total surface area of the whole solid, using the sphere surface area formula A = 4πr² where needed.
- 1Curved hemisphere = 1/2 × 4 × π × 4.3² = 116.1…
- 2Flat circle end = π × 4.3² = 58.0…
- 3Curved cylinder = 2 × π × 4.3 × 11.9 = 321.5…
- 4Total = 116.1… + 58.0… + 321.5… = 495.7… ≈ 496 cm²
Answer496 or 495.7 to 495.8…
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