4MA1/1H Jun 2024, Question 23: Composite Perimeter, Area and Volume
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks
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The question, in short
A cone has a hemisphere removed from its top face; radii are 2x and 5x cm, cone height 6x cm, solid volume 6948π cm³. Find the removed hemisphere's total surface area, to the nearest integer.
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Solution · 5 marks
- 1Cone volume = ⅓π(5x)²(6x) = 50πx³.
- 2Hemisphere volume = ½ × 4/3 × π(2x)³ = 16/3 πx³.
- 350πx³ − 16/3 πx³ = 134/3 πx³ = 6948π, so x³ = 155.55 and x = 5.378.
- 4Solid hemisphere surface = 2πr² + πr² = 3π(2x)² = 12πx².
- 512π × 5.378² = 1090
Answer1090
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