This is the second part of an extensive work on volumetric centers and least partial volumes of proper cones in R n. The first part [cf. Seeger and Torki (Beiträge Algebra Geom, 2014) Centers and partial volumes of convex cones. I: Basic theory] was devoted to presenting the general theory. We now treat some more specialized issues. The notion of least partial volume is a reasonable alternative to the classical concept of solid angle, whereas the concept of volumetric center is an alternative to the old notion of incenter.