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0580/43 May/Jun 2025, Question 18: Trigonometry in 3D: Cuboids

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 8 marks

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The question, in short

For a cuboid measuring 4.5 cm by 8 cm by 13.2 cm, work out its volume, its total surface area, and the angle a space diagonal makes with the base.

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

Part (a) · 1 mark

Find how much space the cuboid occupies using its three side lengths.

  1. 1Volume = 13.2 × 4.5 × 8 = 475.2 cm³

Answer475.2

Part (b) · 3 marks

Work out the combined area of all six rectangular faces of the cuboid.

  1. 113.2 × 4.5 = 59.4, 13.2 × 8 = 105.6, 4.5 × 8 = 36
  2. 2Surface area = 2 × (59.4 + 105.6 + 36) = 2 × 201
  3. 3= 402 cm²

Answer402

Part (c) · 4 marks

Using the space diagonal AB, determine the angle it forms with the horizontal base.

  1. 1Diagonal of the base = √(13.2² + 4.5²) = √194.49 = 13.945…
  2. 2The angle is between AB and the base diagonal, opposite the height 8 cm
  3. 3tan θ = 8 ÷ 13.945…
  4. 4θ = tan⁻¹(0.5736…) = 29.84… ≈ 29.8°

Answer29.8 or 29.83 to 29.84…

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