4MA1/2HR Jan 2022, Question 21: Composite Perimeter, Area and Volume
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 6 marks
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The question, in short
A solid combines a cylinder of height 3x and radius x with a hemisphere of radius x on top; total surface area is 81π cm² and mass 840 g. Use the density table to identify the metal.
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Solution · 6 marks
- 1Surface area = πx² + 2πx × 3x + 2πx² = 9πx²
- 29πx² = 81π, so x² = 9 and x = 3
- 3Volume = π × 3² × 9 + ⅔ × π × 3³ = 81π + 18π = 99π ≈ 311.0 cm³
- 4Density = 840 ÷ 311.0 ≈ 2.70 g/cm³
- 52.7 g/cm³ matches aluminium
Answeraluminium
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