0580/41 May/Jun 2021, Question 9: Composite Perimeter, Area and Volume
Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 11 marks
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The question, in short
For a prism with triangular ends and rectangular base, given AB = 13 cm, AC = 20 cm, CF = 24 cm and a right angle at B, find surface area, volume and the angle AF makes with base BCFE.
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Part (a) · 6 marks
Work out the combined area of all faces of the prism.
- 1BC² = 20² − 13² = 231, BC = 15.19… cm
- 2Two triangles: 2 × 1/2 × 13 × 15.19… = 197.5…
- 3Rectangles: 20 × 24 = 480, 13 × 24 = 312, 15.19… × 24 = 364.7…
- 4Total = 197.5… + 480 + 312 + 364.7… = 1354.3… ≈ 1350 cm²
Answer1350 or 1354…
Part (b) · 1 mark
Work out the space enclosed by the prism.
- 1Volume = 1/2 × 13 × 15.19… × 24 = 2370.9… ≈ 2370 cm³
Answer2370 or 2369 to 2371…
Part (c) · 4 marks
Find the angle between the dashed line AF and the base BCFE.
- 1AB is perpendicular to the base, so the angle is AFB
- 2AF² = 20² + 24² = 976, AF = 31.24…
- 3sin AFB = 13 ÷ 31.24…
- 4Angle = 24.58… ≈ 24.6°
Answer24.6 or 24.58 to 24.59
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