4PM1/01 Jun 2024, Question 4: Connected Rates of Change and Small Changes
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 8 marks
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The question, in short
Sphere surface area grows at 50π cm²/s; find the exact volume in cm³ when the radius increases at 5/12 cm/s.
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Solution · 8 marks
- 1dA/dt = 50π and dr/dt = 5/12
- 2A = 4πr², so dA/dr = 8πr
- 3dr/dt = (dA/dt) ÷ (dA/dr)
- 45/12 = 50π/(8πr), so r = 15
- 5V = (4/3)π × 15³ = 4500π
Answer4500π cm³
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