Volume rate of a widening, shortening cylinder

A cylinder's base radius grows at $2$ m per hour while its height shrinks at $5$ m per hour. When the radius is $3$ m and the height is $6$ m, its volume changes at $k\pi$ cubic metres per hour. Find $k$.

$k=27$. From $V=\pi r^2h$, $V'=2\pi rhr'+\pi r^2h'=2\pi(3)(6)(2)+\pi(9)(-5)=72\pi-45\pi=27\pi$.