0580/22 Feb/Mar 2022, Question 17: Area of a Sector
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 5 marks
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The question, in short
A 4 cm by 11 cm rectangle OPQR has diagonal OQ; a quarter-circle sector centred at O runs from P to X on OQ. Find the shaded region as a percentage of the rectangle.
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Solution · 5 marks
- 1Angle POQ = tan⁻¹(11/4) = 70.01…°
- 2Sector area = 70.01…/360 × π × 4² = 9.776… cm²
- 3Shaded area = 4 × 11 − 9.776… = 34.22… cm²
- 4Percentage shaded = 34.22…/44 × 100 = 77.78… ≈ 77.8%
Answer77.8 or 77.77 to 77.80
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