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0580/21 May/Jun 2026, Question 21: Surface Area of a Cuboid and Cylinder

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Non-calculator · 9 marks

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The question, in short

Cuboid ABCDEFGH has BF = 2 cm, BC = 6 cm, CD = 9 cm. Find its volume, surface area, the length CE, and sin of the angle between CE and base CDHG.

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

Part (a) · 1 mark

Calculate the volume of the cuboid using the three given edge lengths.

  1. 1Volume = 2 × 6 × 9 = 108 cm³

Answer108

Part (b) · 3 marks

Calculate the total surface area of the cuboid.

  1. 1Face areas: 2 × 6 = 12, 2 × 9 = 18, 6 × 9 = 54
  2. 2Sum = 84
  3. 3Surface area = 2 × 84 = 168 cm²

Answer168

Part (c) · 3 marks

Calculate the length of the space diagonal CE.

  1. 1CE² = 2² + 6² + 9²
  2. 2= 4 + 36 + 81 = 121
  3. 3CE = √121 = 11 cm

Answer11

Part (d) · 2 marks

Given the angle between CE and base CDHG is x°, find sin x°.

  1. 1CE = √(2² + 6² + 9²) = √121 = 11 cm
  2. 2E is directly above H, so triangle CHE has a right angle at H.
  3. 3EH = BC = 6 cm is opposite angle x; CE is the hypotenuse.
  4. 4sin x° = 6/11

Answer6/11

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