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The diameter and altitude of a right circular cylinder are found at a certain instant to be 20 cm and 40 cm respectively . If the diameter is increasing at the rate of 2 cm /sec then the rate of change in the altitude will keep the volume constant is

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4 cm/sec

6 cm/sec

–8 cm/sec

2 cm/sec

answer is D.

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Detailed Solution

$r = 10 cm \Rightarrow r = 5 h = 20 cm, \Rightarrow V is constant and \Rightarrow$

$\frac{d}{d t} (2 r) = 2 ∴ \frac{d r}{d t} = 1; V = π r^{2} h$

$\Rightarrow 25 \frac{d h}{d t} = - 200 \Rightarrow \frac{d h}{d t} = - 8$

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