(adsbygoogle = window.adsbygoogle || []).push({}); A water tank is in the shape of an inverted cone with depth 10 meters and top radius 8 meters. Water is flowing into the tank at 0.1 cubic meters/min but leaking out at a rate of 0.001[tex]h^2[/tex] cubic meters/min, where h is the depth of the water in meters. Will the tank ever overflow?Thoughts:

[tex]V=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi (\frac{4}{5}h)^{2}h[/tex]

[tex]\frac{dV}{dt}=\frac{16}{25}\pi h^{2}\frac{dh}{dt}[/tex]

Now I replace [tex]\frac{dV}{dt}[/tex] with 0.1-0.001[tex]h^2[/tex]. This is where I am stuck. Any suggestions?

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Another Related Rates Problem

**Physics Forums | Science Articles, Homework Help, Discussion**