4MA1/2H Jun 2022, Question 20: Composite Perimeter, Area and Volume
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 4 marks
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The question, in short
Four equal circles sit in a square, each touching two circles and two square sides; the shaded area outside the circles is 40 cm². Find the square's perimeter to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1Let r be the radius; the side of the square is 4r
- 2Shaded area = (4r)² − 4πr² = 16r² − 4πr² = 40
- 3r² = 40 ÷ (16 − 4π) = 11.649…, so r = 3.413…
- 4Perimeter = 4 × 4r = 16r = 54.6
Answer54.6
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