4PM1/01 Nov 2021, Question 3: Radians, Arcs and Sectors
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 8 marks
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The question, in short
A sector with integer radius r cm and angle θ radians has area 16.8 cm² and perimeter 16.4 cm. Find r and θ.
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Solution · 8 marks
- 1(i) Area: (1/2)r²θ = 16.8, so θ = 33.6/r²
- 2Perimeter: rθ + 2r = 16.4
- 333.6/r + 2r = 16.4
- 4r² − 8.2r + 16.8 = 0 (5r² − 41r + 84 = 0)
- 5(5r − 21)(r − 4) = 0, r = 4 or 4.2
- 6r is an integer, so r = 4
- 7(ii) θ = 33.6/r² = 33.6/16
- 8θ = 2.1
Answer(i) r = 4; (ii) θ = 2.1
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