Serway & Jewett — Physics and Measurement: Problem 35

Air is blown into a spherical balloon so that, when its radius is $6.50\text{ cm}$, its radius is increasing at the rate $0.900\text{ cm/s}$. (a) Find the rate at which the volume of the balloon is increasing. (b) If this volume flow rate of air entering the balloon is constant, at what rate will the radius be increasing when the radius is $13.0\text{ cm}$? (c) Explain physically why the answer to part (b) is larger or smaller than $0.900\text{ cm/s}$, if it is different.