z>(x^(2)+y^(2))^(1/2) and z<(b^(2)-x^(2)-y^(2))^(1/2) + b where b is some constant
Are you being asked to do it with a triple integral? If I'm reading the constraints correctly (I stink at visualizing in 3D) it is much simpler to integrate over just z using a series of disks.
-Dan