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The slant height of a cone is fixed at 7cm. The rate of increase in the volume of the cone corresponding to the rate of increase of 0.3 cm/s in the height when h = 4cm is ______ cc/sec

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answer is 0.31.

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Detailed Solution

$V = \frac{1}{3} π r^{2} h = \frac{1}{3} π (l^{2} - h^{2}) h = \frac{1}{3} π (l^{2} h - h^{3})$

$\Rightarrow \frac{d v}{d t} = \frac{1}{3} π (l^{2} - 3 h^{2}) \frac{d h}{d t} = \frac{1}{3} π (49 - 3 (4)^{2}) 0.3$

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