Ok, here we go, I'll try to keep this as clear as possible:

We know from previous that V=(1/3)(PI)(h^3)
We are given dV/dt=10 meters cubed per minute.
So.... dV/dt=(PI)(h^2)(dh/dt)
Therefore, dh/dt=(10 meters cubed per minute)/(PI)(h^2)
Now we need to find out what h will equal when the volume is 1000 cubic meters.

(h^3)=(3000)/(PI)
and
h=[the cubed root of(3000)/(PI)], which =9.847
Ok, now comes the rate:
dh/dt=(10 meters cubed per minute)/(PI)(h^2), and we now know what h is, therefore, we plug it in...

dh/dt=(10 meters cubed per minute)/(PI)(9.847 squared), which = (10 meters cubed per minute)/(304.647 meters squared), which = 0.0328 meters per minute.

Now, I'm pretty sure that is correct, but double check me if you want.