I am working with dV/dt = 3*pi*a^3 and dV/da = 2pi*a^2.

dh/dt = (3/2)a

I can see that the height at which it is filled is also the radius a, but I'm not sure how to use the volume given for the shaded part of the hemisphere. Maybe that I should replace h with a/2.....?

How did you get

dV/da = 2pi*a^2? And why do you want that? Since a is a

**constant**, dV/da is irrelevant.

Also,

this is not true, unless you mean merely that a is the depth of the water

**when the bowl is full**; that isn't relevant either.

You want to relate the rate of change of

volume (V) to the rate of change of depth (h).

To do that, they've given you the

volume as a function of depth, so just

**differentiate **that with respect to time. (Radius a is a constant, but you'll use the chain rule to incorporate dh/dt, which is what you'll ultimately solve for.)

(By the way, the radius of the surface of the water isn't relevant, unless you don't want to use the volume formula they gave you.)