The volume $V$ of a right circular cylinder of radius $r$ and height $h$ is $V = \pi r^2 h$.

(a) How is $\frac{dV}{dt}$ related to $\frac{dr}{dt}$ if $h$ is constant and $r$ varies with time? (Enter $\frac{dr}{dt}$ as dr/dt.)
$\displaystyle \frac{dV}{dt} =$

(b) How is $\frac{dV}{dt}$ related to $\frac{dh}{dt}$ if $r$ is constant and $h$ varies with time? (Enter $\frac{dh}{dt}$ as dh/dt.)
$\displaystyle \frac{dV}{dt} =$

(c) How is $\frac{dV}{dt}$ related to $\frac{dh}{dt}$ and $\frac{dr}{dt}$ if both $h$ and $r$ vary with time?
$\displaystyle \frac{dV}{dt} =$