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WMA11/01 Jan 2024, Question 8: Triangles and Sectors in Radians

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 9 marks

The question, in short

Platform plan: sector DOC joined to major sector AOBEA about centre O, with angle AOB = 0.8 radians, arc CD = 9 m and DA : AO = 3 : 5. Find AO, perimeter and total area.

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Part (a) · 3 marks

Show that AO = 7.03 m to 3 significant figures, using arc CD = 9 m, angle 0.8 radians and the ratio DA : AO = 3 : 5.

  1. 1Arc CD: 9 = OD × 0.8
  2. 2OD = 9 ÷ 0.8 = 11.25 m
  3. 3DA : AO = 3 : 5, so AO = (5/8) × OD
  4. 4AO = (5/8) × 11.25 = 7.03125 = 7.03 m (3 s.f.)

AnswerShown: OD = 9 ÷ 0.8 = 11.25 m, AO = (5/8) × 11.25 = 7.03125 ≈ 7.03 m

Part (b) · 3 marks

Calculate the perimeter of the platform in metres to 3 significant figures, including both arcs and the straight edges.

  1. 1Major arc AEB = 7.03125 × (2π − 0.8) = 38.55 m
  2. 2DA = BC = 11.25 − 7.03125 = 4.21875 m
  3. 3Perimeter = 9 + 2 × 4.21875 + 38.55
  4. 4Perimeter = 56.0 m (3 s.f.)

Answer56.0 m

Part (c) · 3 marks

Calculate the total area of the platform in m² to the nearest whole number, combining both sectors.

  1. 1Sector DOC = ½ × 11.25² × 0.8 = 50.625 m²
  2. 2Major sector AOB = ½ × 7.03125² × (2π − 0.8) = 135.54 m²
  3. 3Total = 50.625 + 135.54 = 186.2
  4. 4Area = 186 m² (nearest whole number)

Answer186 m²

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Also searched as: WMA11 January 2024 · WMA11/01 · wma11 jan24 · IAS Maths Pure Mathematics 1 January 2024 · question 8.
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