4MA1/1H Jan 2019, Question 15: Surface Area of a Cuboid and Cylinder
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 4 marks
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The question, in short
A hemisphere of radius r cm has total surface area matching a cylinder's curved area; the cylinder's radius is twice r. Given the volume ratio hemisphere to cylinder is 1:m, determine m.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 4 marks
- 1Hemisphere total surface = 2πr² + πr² = 3πr²; cylinder curved surface = 2π(2r)h = 4πrh
- 23πr² = 4πrh, so h = 3r/4
- 3Hemisphere volume = 2/3 πr³; cylinder volume = π(2r)² × 3r/4 = 3πr³
- 4Ratio = 2/3 πr³ : 3πr³ = 1 : 3 ÷ 2/3
- 5m = 3 × 3/2 = 4.5
Answer4.5
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