4PM1/01 Jun 2025, Question 7: Connected Rates of Change and Small Changes
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 6 marks
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The question, in short
A hemisphere of radius 20 cm drains at constant rate k cm³/s; liquid height h satisfies V = (π/3)h²(60 − h). Given dh/dt = −1/60 when h = 12, find k in terms of π.
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Solution · 6 marks
- 1dV/dt = −k
- 2V = 20πh² − (π/3)h³, so dV/dh = 40πh − πh²
- 3dV/dt = dV/dh × dh/dt
- 4−k = (40π × 12 − π × 144) × (−1/60)
- 5−k = −336π/60, so k = 28π/5
Answerk = 28π/5
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