0580/21 Oct/Nov 2025, Question 12: Area of a Sector
Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Non-calculator · 4 marks
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The question, in short
A sector has radius 9 cm and perimeter (18 + 2π) cm; find its area in terms of π.
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Solution · 4 marks
- 1Arc length = 18 + 2π − 9 − 9 = 2π
- 2θ/360 × 2 × π × 9 = 2π, so θ = 360 × 2π/(18π) = 40°
- 3Area = 40/360 × π × 9²
- 4= 1/9 × 81π = 9π cm²
Answer9π
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