4PM1/02R Jan 2023, Question 7: Volumes of Revolution
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 8 marks
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The question, in short
The curve y = x² + 2 for x ≥ 0 and the line y = a bound region R, which is rotated 360° about the y-axis to give volume 18π. Use algebraic integration to find a.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 8 marks
- 1S meets the y-axis at (0, 2)
- 2x² = y − 2, V = π ∫ from 2 to a of (y − 2) dy
- 318π = π[y²/2 − 2y] from 2 to a
- 418 = (a²/2 − 2a) − (2 − 4)
- 5a² − 4a − 32 = 0
- 6(a + 4)(a − 8) = 0, a > 2 so a = 8
Answera = 8
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