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4PM1/01R Jan 2020, Question 11: Volumes of Revolution

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 11 marks

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The question, in short

Curve C is y = √(x − 2) and line l is y = b, intersecting at P(a, b) with 2 < a < 16; region R between them and x = 16 rotates about the x-axis.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

Show that b² = a − 2 using the intersection of C and l at P(a, b).

  1. 1P(a, b) lies on C, so b = √(a − 2)
  2. 2Square: b² = a − 2

Answerb² = a − 2 shown

Part (b) · 9 marks

Given the solid of revolution from R has volume 50π, use algebraic integration to find a and b.

  1. 1V = π ∫ from a to 16 of (x − 2) dx − π ∫ from a to 16 of (a − 2) dx = π ∫ from a to 16 of (x − a) dx
  2. 2= π[x²/2 − ax] from a to 16 = π(128 − 16a + a²/2)
  3. 3128 − 16a + a²/2 = 50
  4. 4a² − 32a + 156 = 0
  5. 5(a − 6)(a − 26) = 0; a < 16, so a = 6
  6. 6b² = 6 − 2 = 4, b = 2

Answera = 6, b = 2

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