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0580/32 Oct/Nov 2021, Question 7: Composite Perimeter, Area and Volume

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 9 marks

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The question, in short

Work out the area of a compound shape (quarter circle plus trapezium), find a rectangle's missing side from its area, and calculate the volume of a right-angled triangular prism.

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

Part (a) · 4 marks

Find the total area of the shape combining a quarter circle of radius 15 m and a trapezium with parallel sides 15 m and 22 m and height 12 m.

  1. 1Quarter circle = 1/4 × π × 15² = 176.71… m²
  2. 2Trapezium = (15 + 22)/2 × 12 = 222 m²
  3. 3Total = 176.71… + 222 = 398.7… ≈ 399 m²

Answer399 or 398.7…

Part (b) · 2 marks

Given the rectangle's area is 387.1 cm² and its width is 15.8 cm, find the length h.

  1. 1Area = length × width, so 15.8 × h = 387.1
  2. 2h = 387.1 ÷ 15.8 = 24.5

Answer24.5

Part (c) · 3 marks

Find the volume of the prism whose triangular end has perpendicular sides 15 cm and 18 cm and whose length is 32 cm.

  1. 1Triangle area = 1/2 × 15 × 18 = 135 cm²
  2. 2Volume = 135 × 32 = 4320 cm³

Answer4320

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Also searched as: 0580/32/O/N/21 · 0580_w21_qp_32 · 0580 w21 32 · question 7.
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