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4024/21 Oct/Nov 2020, Question 5: Surface Area of a Cuboid and Cylinder

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 11 marks

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The question, in short

A shed is a prism with a trapezium cross-section (1.55, 2.25, 1.85 m) and length 2.10 m: find its volume, the paint for its sloping roof and an angle of elevation.

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

Part (a) · 3 marks

Area of the trapezium times the length.

  1. 1Area of trapezium ABCD = 1/2 × (2.25 + 1.85) × 1.55 = 3.1775 m²
  2. 2Volume = 3.1775 × 2.10
  3. 3= 6.672… ≈ 6.67 m³

Answer6.67 or 6.672 to 6.673

Part (b) · 4 marks

Find the slant edge, then the roof area, at 2 m² per litre.

  1. 1DC² = 1.55² + (2.25 − 1.85)² = 2.4025 + 0.16 = 2.5625
  2. 2DC = 1.6007… m
  3. 3Roof area = 1.6007… × 2.1 = 3.3616… m²
  4. 4Paint = 3.3616… ÷ 2 = 1.680… litres

Answer1.68 to 1.681...

Part (c) · 4 marks

Angle of elevation of D from F in 3D.

  1. 1AF² = 1.55² + 2.1² = 2.4025 + 4.41 = 6.8125, AF = 2.6100… m
  2. 2Angle DAF = 90°, so tan DFA = 2.25/2.6100…
  3. 3Angle of elevation = 40.76… ≈ 40.8°

Answer40.8 or 40.76…

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