4PM1/01 Nov 2021, Question 6: 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 sphere's volume grows at a steady 3 cm³/s; find how fast its surface area grows, in cm²/s, at the instant r = 10 cm.
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Solution · 6 marks
- 1V = (4/3)πr³, dV/dr = 4πr²
- 2A = 4πr², dA/dr = 8πr
- 3dA/dt = dA/dr × dr/dV × dV/dt
- 4= 8π(10) × 1/(4π × 10²) × 3
- 5= 0.6 cm²/s
Answer0.6 cm²/s
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