A sphere with radius 10 cm is being filled at a rate of 1 cm3 per minute. What rate is the depth of the water increasing when it is 5 cm?
So what I did was:
$r=10$ $\frac{dV}{dt} = 1$ $d = 5$ $V= \frac{4}{3}\pi r^2$ $\frac{dV}{dt} = \frac{8}{3}\pi r \frac{dr}{dt}$
However, what I'm really looking for isn't $\frac{dr}{dt}$ but instead $\frac{dD}{dt}$, and I can't think of any way to relate volume to depth or radius. How can I do this?