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WMA11/01 Jun 2022, Question 8: Radians, Arcs and Sectors

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 10 marks

The question, in short

For a ceiling fan face made of three congruent sections OABCDO with inner radius 9 cm and outer radius 84 cm, angle AOD = 2π/3 and arc AB = 15 cm, find arc CD, the fan perimeter and the face area.

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

Part (a) · 3 marks

Using arc AB = 15 cm on the 9 cm circle, determine the angle AOB, then use it to calculate the length of arc CD on the 84 cm circle, showing 35.9 cm.

  1. 115 = 9θ, so angle AOB = θ = 5/3
  2. 2Angle COD = 2π/3 − 5/3 = 0.4277…
  3. 3Arc CD = 84 × 0.4277… = 35.929… = 35.9 cm

AnswerShown: angle AOB = 5/3, angle COD = 2π/3 − 5/3 = 0.4277…, arc CD = 84 × 0.4277… = 35.929… = 35.9 cm

Part (b) · 2 marks

Calculate the total distance around the outside of the fan face, using the straight and curved edges of all three sections, to the nearest cm.

  1. 1Each section: arc AB 15, two straight edges of 84 − 9 = 75, arc CD 35.93
  2. 2Perimeter = 3(15 + 35.93) + 6 × 75 = 602.8 ≈ 603 cm

Answer603 cm

Part (c) · 5 marks

Calculate the total area of the fan face from its three congruent sections, giving 3 significant figures with units.

  1. 1Blade sector: ½ × 84² × (2π/3 − 5/3) = 1509.0… cm²
  2. 2Small sector between blades: ½ × 9² × 5/3 = 67.5 cm²
  3. 3Total = 3(1509.0… + 67.5) = 4729.6 cm²
  4. 4Area ≈ 4730 cm² (0.473 m²)

Answer4730 cm² (or 0.473 m²)

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Also searched as: WMA11 June 2022 · WMA11/01 · wma11 jun22 · IAS Maths Pure Mathematics 1 June 2022 · question 8.
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