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0580/41 Oct/Nov 2024, Question 9: Angle Between a Line and a Plane

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 12 marks

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The question, in short

For a cuboid ABCDEFGH with AB = 10 cm, BC = 8 cm and CG = 17 cm, find its volume, surface area, the angle between GA and base ABCD, and the length of rod PQ.

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

Part (a) · 1 mark

Find the volume of the cuboid.

  1. 1Volume = 10 × 8 × 17 = 1360 cm³

Answer1360

Part (b) · 3 marks

Find the total surface area of the cuboid.

  1. 1Faces: 10 × 8 = 80, 10 × 17 = 170, 8 × 17 = 136
  2. 2Total surface area = 2 × (80 + 170 + 136)
  3. 3= 2 × 386 = 772 cm²

Answer772

Part (c) · 4 marks

Find the angle that GA makes with the base ABCD.

  1. 1The angle required is angle GAC
  2. 2AC = √(10² + 8²) = √164 = 12.806… cm
  3. 3tan GAC = 17/√164 = 1.327…
  4. 4Angle GAC = 53.00… ≈ 53°

Answer53 or 53.0 to 53.01

Part (d) · 4 marks

P is the midpoint of AB and Q lies on GH with HQ : QG = 4 : 1. Find the length of PQ.

  1. 1QG = 10 × 1/5 = 2 cm, HQ = 8 cm
  2. 2Along AB the ends differ by 5 − 2 = 3 cm; across BC by 8 cm; up by 17 cm
  3. 3PQ = √(3² + 8² + 17²) = √362
  4. 4PQ = 19.02… ≈ 19.0 cm

Answer19.0 or 19.02 to 19.03

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Also searched as: 0580/41/O/N/24 · 0580_w24_qp_41 · 0580 w24 41 · question 9.
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