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0580/43 May/Jun 2023, Question 9: Angle Between a Line and a Plane

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 10 marks

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The question, in short

For a shape combining an 11 cm square with two equal quarter-circle sectors, find its area and perimeter; then for a 7 cm cube, find the angle between diagonal AG and the base.

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

Part (ai) · 3 marks

Calculate the total area of the square plus the two sectors, using side 11 cm.

  1. 1Square = 11 × 11 = 121
  2. 2Each sector is a quarter circle radius 11: 1/4 × π × 11² = 95.03…
  3. 3Area = 121 + 2 × 95.03… = 311.1 cm²

Answer311 or 311.0 to 311.1

Part (aii) · 3 marks

Calculate the total perimeter of the shape, including the two arcs.

  1. 1Straight edges MB and DN: 22 + 22 = 44
  2. 2Each arc = 1/4 × 2π × 11 = 17.28…
  3. 3Perimeter = 44 + 2 × 17.28… = 78.56 cm

Answer78.6 or 78.55 to 78.56…

Part (b) · 4 marks

Calculate the angle between the space diagonal AG and the base of the 7 cm cube.

  1. 1The angle required is angle GAC
  2. 2AC = √(7² + 7²) = 9.899…
  3. 3tan GAC = 7/9.899…
  4. 4Angle = 35.26° ≈ 35.3°

Answer35.2 or 35.3 or 35.239… to 35.28

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Also searched as: 0580/43/M/J/23 · 0580_s23_qp_43 · 0580 s23 43 · question 9.
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