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Question

The radius of a cylinder is increasing at the rate of 5 cm/min so that its volume is constant. When its radius is 5 cm and height is 3 cm, then the rate of decreasing of its height is

A
6 cm/min
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B
3 cm/min
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C
4cm/min
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D
5 cm/min
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E
2 cm/min
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Solution

The correct option is A 6 cm/min
Let V be volume of the cylinder.
Given that:
drdt=5cm/min , r=5 cm and h=3 cm
We know that,
V=πr2h
Differentiating it wrt t, we get
dVdt=π×2r×drdt×h+πr2×dhdt
Since, V is constant dVdt=0
0=π×2r×drdt×h+πr2×dhdt
2hdrdt=rdhdt
5dhdt=2×3×5 cm/min
dhdt=6 cm/min
Rate of decreasing of height,(dhdt)=6 cm/min
Hence, A is the correct option.

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