There is a formula for the volume of a sphereical cap as given in my earlier post and the volume of this solid can be written as a sum of the volumes of two spherical caps (as I may have already mentioned).
The calculus comment is an irrelevance, most people are incapable of deriving either formula without the aid of claculus (while Archimedes could derive both without modern calculus, but then he had invented his own form of integral calculus in the method of exahuastion).
CB