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4PM1/01R Jun 2020, Question 7: Connected Rates of Change and Small Changes

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 9 marks

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The question, in short

Cube S₁ has side length growing at 0.1 m/s; cube S₂ has total surface area growing at 0.05 m²/s. Find the rate of increase of volume of each cube at the stated side lengths.

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

Part (a) · 4 marks

For S₁, with side increasing at 0.1 m/s, find the volume's rate of increase in m³/s when the side is 2 m.

  1. 1V = x³ ⇒ dV/dx = 3x² = 12 at x = 2
  2. 2dx/dt = 0.1
  3. 3dV/dt = dV/dx × dx/dt = 12 × 0.1
  4. 4= 1.2 m³/s

Answer1.2 m³/s

Part (b) · 5 marks

For S₂, with surface area increasing at 0.05 m²/s, find the volume's rate of increase in m³/s when the side is 6 m.

  1. 1A = 6x² ⇒ dA/dx = 12x = 72 at x = 6
  2. 2dV/dx = 3x² = 108, dA/dt = 0.05
  3. 3dV/dt = dV/dx × dx/dA × dA/dt = 108 × (1/72) × 0.05
  4. 4= 0.075 m³/s

Answer0.075 m³/s

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