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Question

The radius of a right circular cylinder increases at the rate of 0.1cm/min, and the height decreases at the rate of 0.2cm/min. The rate of change of the volume of the cylinder, in cm3/min., when the radius is 2cm and the height is 3cm is

A
2p
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B
8π5
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C
3π5
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D
2π5
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Solution

The correct option is D 2π5
Volume of cylinder V=πr2h
dVdt=π(r2dhdt+2rhdrdt)
dVdt=0.4π
dVdt=2π5cm3/min

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