SI. 2 If the height of a cylinder is doubled and the new radius is $h$ times the original, then the new volume is $k$ times the original. Find $k$.
Let the old height be $x$, old radius be $r$, then the old volume is $\pi r^{2} x$. The new height is $2 x$, the new radius is $4 r$, then the new volume is $\pi(4 r)^{2}(2 x)=32 \pi r^{2} x$
$$
k=32
$$