I need to find the volume of region bounded above by sphere and below by the inverted cone and also find the centre of gravity with density equalling constant.

I set up my bound and triple integral as

and after solving i got approx 28.60

using symetry, the centre of gravity is on the z axis and using the formula for centre of mass:

and subsituting above result and

i obtained

solving with bounds stated in first part i got

does this look correct? thanks for any help.