4MA1/1H Jun 2022, Question 22: 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 and hemisphere share a 20 cm radius base; the cone's curved area is 580π cm². Find k where the solid's volume is kπ cm³.
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Solution · 5 marks
- 1580π = π × 20 × l
- 2l = 580π / (π × 20) = 29
- 3h² = 29² − 20² = 841 − 400 = 441
- 4h = √441 = 21
- 5(1/3) × π × 20² × 21 + (1/2) × (4/3) × π × 20³
- 6(1/3) × π × 400 × 21 + (1/2) × (4/3) × π × 8000
- 72800π + (16000π)/3
- 8(8400π)/3 + (16000π)/3 = 24400π/3
- 9k = 24400/3
Answer24400/3
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