4PM1/02 Jan 2020, Question 10: Connected Rates of Change and Small Changes
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 9 marks
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The question, in short
Given a sphere's volume grows at 40 cm³/s, find how fast its surface area increases in cm²/s when the radius equals 4 cm.
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Solution · 9 marks
- 1dV/dt = 40
- 2A = 4πr², so dA/dr = 8πr
- 3V = (4/3)πr³, so dV/dr = 4πr²
- 4dA/dt = dA/dr × dr/dV × dV/dt = 8πr × 1/(4πr²) × 40 = 80/r
- 5r = 4: dA/dt = 20 cm²/s
Answer20 cm²/s
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