4PM1/01 Jun 2025, Question 11: Volumes of Revolution
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 7 marks
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The question, in short
The curve y = √(4x − 8) and the line x = b bound a shaded region rotated 360° about the x-axis; given the solid's volume is 50π units³, find b.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 7 marks
- 1C meets the x-axis where 4x − 8 = 0, x = 2
- 2V = π ∫ from 2 to b of (4x − 8) dx
- 3= π[2x² − 8x] from 2 to b = π(2b² − 8b + 8)
- 42b² − 8b + 8 = 50, so b² − 4b − 21 = 0
- 5(b + 3)(b − 7) = 0, b > 0 gives b = 7
Answerb = 7
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