4PM1/02R Jan 2023, Question 6: 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 sector has fixed angle π/6 and radius r growing at 0.2 cm/s; find the exact rate at which its area grows when arc AB measures 5π/2 cm.
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Solution · 6 marks
- 1A = ½r²(π/6) = πr²/12
- 2dA/dr = πr/6
- 3Arc AB = r(π/6) = 5π/2 → r = 15
- 4dA/dt = dA/dr × dr/dt = (π × 15/6) × 0.2
- 5= π/2 cm²/s
Answerπ/2 cm²/s
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