4PM1/02 Jun 2023, Question 3: Radians, Arcs and Sectors
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 6 marks
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The question, in short
From a shaded major sector with area 372.4 cm² and arc length 53.2 cm, find the radius r and the obtuse angle θ in radians, giving values to 3 significant figures where appropriate.
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Solution · 6 marks
- 1Let α be the reflex angle AOB of the shaded sector, so α = 2π − θ
- 2Arc: rα = 53.2; area: (1/2)r²α = 372.4
- 3(1/2)r × (rα) = 372.4, so (1/2)r × 53.2 = 372.4, r = 14
- 4α = 53.2/14 = 3.8
- 5θ = 2π − 3.8 = 2.48
Answer(i) r = 14 (ii) θ = 2.48
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