4PM1/01 Jan 2020, Question 4: Radians, Arcs and Sectors
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 6 marks
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The question, in short
A sector AOB has radius r cm and angle 0.8 rad; O, A, C are collinear and CB is tangent at B. Given the shaded area between arc AB and lines AC, CB is 101 cm², find r to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1Area of sector = ½r² × 0.8 = 0.4r²
- 2Angle OBC = 90° (tangent ⟂ radius), so BC = r tan 0.8
- 3Area of triangle OBC = ½ × r × r tan 0.8
- 4Shaded area: ½r² tan 0.8 − 0.4r² = 101
- 5r² = 101/(½ tan 0.8 − 0.4) = 879.6…
- 6r = 29.658… = 29.7
Answerr = 29.7
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