4MA1/2H Nov 2021, Question 22: Surface Area of a Pyramid
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 6 marks
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The question, in short
A sphere has diameter x cm and volume 288π cm³. A pyramid has rectangular base BCDE with BC = x cm, CD = 2x cm, apex A vertically above centre O with AO = 5x cm. Find the pyramid's total surface area to the nearest cm².
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Solution · 6 marks
- 1Sphere: 4/3 × π × (x/2)³ = 288π, so x³ = 1728 and x = 12
- 2Base 12 × 24 = 288 cm²; height AO = 60 cm
- 3Faces on the 24 cm sides: slant height √(60² + 6²) = √3636, two faces = 24 × √3636 = 1447.2…
- 4Faces on the 12 cm sides: slant height √(60² + 12²) = √3744, two faces = 12 × √3744 = 734.2…
- 5Total = 288 + 1447.2… + 734.2… = 2469 cm²
Answer2469
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