4MA1/1H Jun 2021, Question 25: Composite Perimeter, Area and Volume
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 6 marks
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The question, in short
Two circles with centres O and P, radii 5 cm and 4 cm, intersect at A and B with angle AOB = 50°. Find the shaded common area R to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1Chord AB = 2 × 5 × sin 25° = 4.2262 cm
- 2In the smaller circle, 4.2262 = 2 × 4 × sin(APB ÷ 2), so angle APB = 63.776°
- 3Segment in circle O = sector − triangle = (50/360) × π × 5² − 0.5 × 5 × 5 × sin 50°
- 4That is 10.908 − 9.576 = 1.3328 cm²
- 5Segment in circle P = (63.776/360) × π × 4² − 0.5 × 4 × 4 × sin 63.776°
- 6That is 8.905 − 7.178 = 1.7266 cm²
- 7Region R = 1.3328 + 1.7266 = 3.0594
- 8To 3 significant figures that is 3.06 cm²
Answer3.06
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