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Question

A balloon which always remains spherical, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon is increasing when the radius is 15 cm.

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Solution

Let r be the radius and V be the volume of the spherical balloon at any time t. Then, V=43πr3dVdt=4πr2drdtdrdt=14πr2dVdtdrdt=9004π152 r=15 cm and dVdt=900 cm3/secdrdt=900900πdrdt=1πcm/sec

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