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0606/12 May/Jun 2025, Question 10: Radians, Arcs and Sectors

Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 8 marks

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The question, in short

Using sectors with centre O and radii r and 4r/3, with BE parallel to AOF and angle COD θ, find the shaded area BCDE and the perimeter of region OABEF in terms of r and θ.

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

Part (a) · 3 marks

Find the area of the shaded region BCDE in terms of r and θ.

  1. 1Area of sector OCD = (1/2)(4r/3)²θ = (8/9)r²θ
  2. 2Area of triangle OBE = (1/2)r² sin θ
  3. 3Shaded area = (1/2)(4r/3)²θ − (1/2)r² sin θ

Answer(1/2)(4r/3)²θ − (1/2)r² sin θ

Part (b) · 5 marks

Find the perimeter of the shaded region OABEF in terms of r and θ.

  1. 1Angle BOA = angle EOF = (π − θ)/2
  2. 2Arc length AB = r(π − θ)/2, so arcs AB + EF = r(π − θ)
  3. 3BE² = r² + r² − 2r² cos θ, so BE = √(2r²(1 − cos θ)) (= 2r sin(θ/2))
  4. 4Perimeter = OA + OF + arcs + BE = 2r + r(π − θ) + √(2r²(1 − cos θ))

Answerr(π − θ) + 2r + √(2r²(1 − cos θ))

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Also searched as: 0606/12/M/J/25 · 0606_s25_qp_12 · 0606 s25 12 · question 10.
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