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0580/21 May/Jun 2025, Question 13: Composite Perimeter, Area and Volume

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Non-calculator · 8 marks

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The question, in short

Compare total surface areas of a cone-on-hemisphere solid and a cylinder; radius 6 cm, cone slant edge 10 cm, cylinder radius 4 cm. Find cylinder height h and solid A's height.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 5 marks

Given equal total surface areas of solid A and solid B, calculate the cylinder height h in cm.

  1. 1Solid A: cone curved surface = π × 6 × 10 = 60π; hemisphere = 2 × π × 6² = 72π
  2. 2Total for A = 132π
  3. 3Solid B: 2 × π × 4² + 2 × π × 4 × h = 32π + 8πh
  4. 432π + 8πh = 132π, so 8πh = 100π
  5. 5h = 12.5

Answer12.5

Part (b) · 3 marks

Calculate the overall height of solid A from its hemisphere and cone dimensions.

  1. 1Cone height = √(10² − 6²) = √64 = 8
  2. 2Height of A = 8 + 6 = 14 cm

Answer14

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