I'm mostly interested in one where a=b=2c e.i. a ball that has been "sqeesed". the sphere is "standing" on the large diameter the other one i know Its difficult to explain but i want to calculate the volume of a vessel with spherical end caps. The cylinder is easy and i could cheat and either say the the vessel was 0.5*diameter longer and assume flat ends or that the end caps was normal spheres - but i know that they have said geometry.
The volume should then be a function of how full the shere is. Its OK if the formular only "works" (for geometrical reasons) up to half full.