Related Rates and a Conical Tank

Jacobpm64

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 0.001h² cubic meters/min, where h is the depth of the water in the tank in meters. Can the tank ever overflow?

Can anyone help with this? The flowing in and leaking out is a bit confusing.

courtrigrad

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


You know that [tex] \frac{r}{h} = \frac{4}{5} [/tex], so [tex] r = \frac{4h}{5} [/tex]

So the new expression is: [tex] V = \frac{1}{3}\pi (\frac{4h}{5})^{2}h = \frac{16\pi}{75}h^{3} [/tex]

You also know that [tex] \frac{dV}{dt} = 0.1 - 0.001 [/tex]