4MA1/1H Jun 2023, Question 22: 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
A regular pentagon ABCDE with side 8 cm sits inside a larger circle centre O; a smaller circle centre O is shaded so shaded area equals unshaded area. Find the smaller circle's radius to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1Large radius R = 4 ÷ sin 36° = 6.805…, so circle area = πR² = 145.49…
- 2Pentagon area = 5 × ½ × 8 × (4 × tan 54°) = 110.11…
- 3Unshaded = pentagon − small circle; shaded = small circle + (circle − pentagon)
- 4Equal areas: 110.11 − πr² = πr² + 35.38, so 2πr² = 74.73…
- 5r² = 11.89…, so r = 3.45
Answer3.45
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