You can set up an integral using washers.
Evaluate the integral and it'll give the volume at any height h.
The original function forms the equation for a circle, The square of 15 is 225.
It's -15 because if the diameter of the hemisphere is centered at the origin,the bottom would be at -15. Then, any height above that would be
h-15.
If you left h=15, you would get the full volume of the hemisphere.