The motivation for related rates is expressing one rate in terms of another. This is useful because some object's propriets are easier to measure than others. A famous textbook example is the spherical baloon one. It's way easier to measure the baloon volume than the radius of the baloon. If you need to know the rate at which the radius is growing you can derivate a formula for this from the volume formula.

So, for (a):

In (b), you want to know how these quantities vary over TIME. But first you need to know what's the relation between the variation of V and h:

Now derivating with respect to time (remember that V is a function of h, so you use the chain rule):

(I) gives you dV/dh, and the problem statement gives you :

It should be clear from now on. I hope I didn't make any major mistake in my explanations or calculations, since I don't see this subject for a while now.

Regards,