4MA1/2HR Jan 2019, Question 22: Area of a Sector
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 6 marks
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The question, in short
Two sectors share centre O with angle 45°; OA:AP = OB:BQ = 3:2 and the shaded region between the arcs has area (81/2)π cm². Find the shaded region's perimeter in terms of π.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1Let OP = r, so OA = 3r/5
- 2Shaded area = (45/360)π(r² − 9r²/25) = (2/25)πr²
- 3(2/25)πr² = (81/2)π gives r² = 506.25, so r = 22.5
- 4OA = 13.5, so arcs = (1/8)(45π) + (1/8)(27π) = 9π
- 5Straight sides AP + BQ = 9 + 9, so perimeter = 9π + 18
Answer9π + 18
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