Originally Posted by
HallsofIvy You are given that the volume of cylinder of radius r and height h is $\displaystyle \pi r^2h$, that $\displaystyle h= \frac{10}{\pi r^2}$ and that $\displaystyle r= 3+ 2sin(t)$.
ONE way to do this is to replace h in the volume formula with that formula in terms of r:
$\displaystyle V= \pi r^2h= \pi r^2\frac{10}{\pi r^2}= 10$ and then replace "r" in that by its formula in terms of t.
Oh, wait- there is no "r" in that formula- the "$\displaystyle \pi r^2$" terms canceled out and we got V= 10, a constant! Well, what does that tell you about its derivative?