4MA1/2HR Jun 2025, Question 26: Volume and Surface Area of a Sphere
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 5 marks
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The question, in short
A solid hemisphere H has radius x cm and volume 6174π cm³. A bowl is formed by removing a hemisphere so the bowl has uniform thickness 2 cm. Find the bowl's total surface area in terms of π.
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Solution · 5 marks
- 11/2 × 4/3 × π × x³ = 6174π, so x³ = 9261 and x = 21
- 2Inner radius = 21 − 2 = 19 cm
- 3Curved surfaces: 2π × 21² + 2π × 19² = 882π + 722π
- 4Flat ring on top: π × 21² − π × 19² = 80π
- 5Total = 882π + 722π + 80π = 1684π
Answer1684π
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