Generally speaking you find "related rates" by starting with a formula relating the things them selves, then differentiating with respect to time, t, to get a formula relating there rates.

Here, you are asked about the rate of change of the volume in a sphere with respect to height (or depth). So: if you have a spherical "goldfish bowl", of radius R, filled with water up to height z, what is the volume of the water? One way to do that is to start with the fact that the boundary of the sphere can be modeled as and convert to cylindrical coordinates: [itex]r^2+ z^2= R^2[/itex] and integrate from z=0 to z= Z: .