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4PM1/02 Jun 2023, Question 6: Connected Rates of Change and Small Changes

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 6 marks

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The question, in short

For a right triangular prism with equilateral cross-section sides r and length 5, show its volume formula, then find the rate of volume increase given side growth and a face area.

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

Part (a) · 1 mark

Show that the prism volume equals (5√3/4)r² cm³ using the given triangle dimensions and prism length.

  1. 1Area of triangle ABC = (1/2)r² sin(π/3) = (√3/4)r²
  2. 2V = 5 × (√3/4)r² = (5√3/4)r²

AnswerV = (5√3/4)r² shown

Part (b) · 5 marks

With r increasing at 0.2 cm/s, find the exact rate of volume increase when rectangular face BCDF has area 60 cm².

  1. 1dV/dr = (5√3/2)r
  2. 2Triangle ABC is equilateral, so BC = r; area BCDF = 5r = 60, r = 12
  3. 3dV/dt = dV/dr × dr/dt
  4. 4= (5√3/2) × 12 × 0.2
  5. 5= 6√3 cm³/s

Answer6√3 cm³/s

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