4PM1/02R Jun 2019, Question 3: Connected Rates of Change and Small Changes
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 6 marks
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The question, in short
A cylindrical rod has diameter x cm and length 10x cm; its length grows at 0.005 cm/s. Find the rate of increase of volume in cm³/s to 2 significant figures when x = 3.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1l = 10x ⇒ dl/dx = 10, so dx/dt = 0.005 ÷ 10 = 0.0005
- 2V = π(x/2)² × 10x = 5πx³/2
- 3dV/dx = 15πx²/2
- 4dV/dt = dV/dx × dx/dt = (15π × 3²/2) × 0.0005
- 5= 0.10603… ≈ 0.11 cm³/s
AnswerdV/dt = 0.11 cm³/s
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