Related Rates of Change Question

[Charismaztex]

Homework Statement

A spherical tank with an interior diameter of 2m is being filled with water at a rate of 10 liters per second. Determine what rate the height of the water is increasing at when the tank is half full.

Homework Equations

$$V=\frac{2\pi r^3}{3}-\pi r^2d+\frac{\pi d^3}{3}$$

Where r is the radius of the sphere and d is the distance from the surface of the water to the top of the hemisphere.

The Attempt at a Solution

We want to find $$\frac{dh}{dt}$$ but we need another variable to use the chain rule. So I suppose we need to use $$\frac{dh}{dt}=\frac{dh}{dV}X\frac{dV}{dt}$$
as we've got the rate of volume fill per second (10 liters per second). So how would I go about making h in terms of v?

Thanks,
Charismaztex

 

[LCKurtz]

You may well be expected to derive it, but you will find the correct formula for the volume of a spherical cap in terms of its height h at

http://en.wikipedia.org/wiki/Spherical_cap