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A balloon which always remains spherical on inflation is being Inflated by pumping in $900$ cubic centimeter of gas per second. find the rate at which the radius of balloon increases when the radius is $15 c m$ .

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Detailed Solution

Given $\frac{d v}{d t} = 900 {cm}^{3} / \sec r = 15 cm$

Volume of sphere $(V) = \frac{4}{3} π r^{3}$

$\frac{d v}{d t} = \frac{4}{3} π (3 r^{2}) \frac{d r}{d t} \Rightarrow 900 = \frac{4}{3} π 3 (15)^{2} \frac{d r}{d t}$

$\frac{d r}{d t} = \frac{1}{π} cm / \sec$

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