The Chain Rule: Videos & Practice Problems

A spherical balloon's volume changes with temperature at a rate directly proportional to its volume. The volume $V$ of the balloon can be expressed as $V=\frac{4}{3}\pi r^3$, where $r$ is the radius of the balloon, and $r$ is a function of temperature $T$. The rate of change of the radius with respect to temperature is given by $\frac{dr}{dT}=kr$, where $k$ is a proportionality constant. Determine the rate, in terms of $V$, at which the volume changes with respect to the temperature.