Optimization: water pumped into inverted conical tank

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The height and top diameter of an inverted conical tank are 1 and 4 meters respectively. Water is being pumped into this tank at a rate of p cm^3/min and is leaking at a rate of q cm^3/min, with q < p. The water leve is rising at a rate of r cm^2/min when the height of the water is s meters.

(1) If q, r, and s are given, find p.
(2) If p, r, and s are given, find q.
(3) If p, q, and s are given, find r.
 
Start by using similar triangles to eliminate a variable.

For instance,

\(\displaystyle \frac{r}{h}=\frac{\frac{1}{2}}{4}\)

\(\displaystyle r=\frac{h}{8}\)

\(\displaystyle V=\frac{1}{3}{\pi}r^{2}h\)

\(\displaystyle V=\frac{1}{3}{\pi}(\frac{h^{3}}{64})\)

Also, check this link for a similar problem.

http://www.freemathhelp.com/forum/viewtopic.php?t=17866
 
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