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4024/13 May/Jun 2025, Question 20: Area of a Sector

Cambridge O Level Mathematics 4024 · Paper 13 (Non-calculator) · Non-calculator · 6 marks

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The question, in short

Two sectors with centre O and angle 60°, radii 6 cm and 9 cm, form a shaded region between their arcs; find constants in its perimeter and its area in terms of π.

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Part (a) · 3 marks

The shaded region's perimeter equals aπ + b cm; find the values of a and b.

  1. 1Arc CD = 60/360 × 2π × 9 = 3π
  2. 2Arc AB = 60/360 × 2π × 6 = 2π
  3. 3Straight edges AC and BD = 9 − 6 = 3 each, so 2 × 3 = 6
  4. 4Perimeter = 3π + 2π + 6 = 5π + 6
  5. 5a = 5, b = 6

Answera = 5, b = 6

Part (b) · 3 marks

Calculate the area of the shaded region, giving the answer in simplest form in terms of π.

  1. 1Large sector = 60/360 × π × 9² = 81π/6
  2. 2Small sector = 60/360 × π × 6² = 36π/6
  3. 3Shaded area = 81π/6 − 36π/6 = 45π/6
  4. 4= 15π/2 cm²

Answer15π/2 or 7.5π

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Also searched as: 4024/13/M/J/25 · 4024_s25_qp_13 · 4024 s25 13 · question 20.
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