Optimization: water pumped into inverted conical tank

[Guest]

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.

 

[galactus]

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

 

[Guest]

ok

Thanks for the tip.