V = (3-(r^2/3))h and h/(2-r) = 5/2
Write V as a function of H.
Simplify the function so that you can express it as a polynomial in H.
$\displaystyle V=(3-r^{\frac{2}{3}})h$
$\displaystyle \frac{h}{2-r}=\frac{5}{2}$
Rearranging gives:
$\displaystyle h=\frac{5(2-r)}{2}$
$\displaystyle 2h=10-5r$
$\displaystyle 2h-10=-5r$
$\displaystyle r=\frac{10-2h}{5}$
$\displaystyle r=2-\frac{2h}{5}$
Now substitute the second one into the first one and you're home dry!