Multivariable problem involving integrals

I'm having problems with this and was looking for some insight.

*"Randy is going to use a porcelain bowl to measure rain. The bowl has the shape $\displaystyle z=x^2+y^2$ from $\displaystyle z=0$ to $\displaystyle z=10$ inches. Randy must calibrate the bowl so that he can precisely measure the amount of rain that falls. ***What height of water in the bowl corresponds to an inch of rain?** That is to say, a circular cylinder would have one inch of rain in it, or that the level ground would have standing water one inch deep."

Are there any ideas?