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WMA11/01 Jun 2023, Question 5: Radians, Arcs and Sectors

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

The question, in short

For a garden plan OABCD with OA = 4 m, OD = 6 m, CD = 1.5 m, arc AB centred at O, find angle AOB, then the perimeter and area.

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

Part (a) · 2 marks

Show that angle AOB equals 1.186 radians, correct to 4 significant figures.

  1. 1B is 1.5 m above OD (same height as C), and OB = 4 m
  2. 2Angle AOB is measured from the vertical, so cos(AOB) = 1.5/4
  3. 3AOB = cos⁻¹(0.375) = 1.18639… = 1.186 radians

AnswerShown: cos(AOB) = 1.5/4, so angle AOB = 1.186 radians (4 s.f.)

Part (b) · 4 marks

Calculate the garden's perimeter in metres, giving the result to 3 significant figures.

  1. 1Arc AB = rθ = 4 × 1.186 = 4.744 m
  2. 2Horizontal distance from O to B = √(4² − 1.5²) = √13.75 = 3.708 m
  3. 3BC = 6 − 3.708 = 2.292 m
  4. 4Perimeter = 4.744 + 2.292 + 1.5 + 6 + 4 = 18.5 m

Answer18.5 m

Part (c) · 4 marks

Calculate the garden's area in square metres, giving the result to 3 significant figures.

  1. 1Sector AOB = ½ × 4² × 1.186 = 9.49 m²
  2. 2OBCD is a trapezium with parallel sides BC = 2.292 and OD = 6, height 1.5
  3. 3Area OBCD = ½ × (6 + 2.292) × 1.5 = 6.219 m²
  4. 4Total area = 9.49 + 6.219 = 15.7 m²

Answer15.7 m²

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Also searched as: WMA11 June 2023 · WMA11/01 · wma11 jun23 · IAS Maths Pure Mathematics 1 June 2023 · question 5.
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