4MA1/1H Jun 2022, Question 19: Area of a Sector
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks
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The question, in short
Sector S has radius (r + 7) m and angle 45°; circle C has radius (r − 2) m. Given sector area is twice circle area, find r showing working.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1Sector area = (45/360) × π(r + 7)²; circle area = π(r − 2)²
- 2(1/8)(r + 7)² = 2(r − 2)², so (r + 7)² = 16(r − 2)²
- 3r² + 14r + 49 = 16r² − 64r + 64, so 15r² − 78r + 15 = 0
- 45r² − 26r + 5 = 0 gives (5r − 1)(r − 5) = 0
- 5r = 1/5 makes r − 2 negative, so r = 5
Answer5
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