We calculate the volumes of a large class of Einstein manifolds, namely
Sasaki-Einstein manifolds which are the bases of Ricci-flat affine cones
described by polynomial embedding relations in C^n. These volumes are important
because they allow us to extend and test the AdS/CFT correspondence. We use
these volumes to extend the central charge calculation of Gubser (1998) to the
generalized conifolds of Gubser, Shatashvili, and Nekrasov (1999). These
volumes also allow one to quantize precisely the D-brane flux of the AdS
supergravity solution. We end by demonstrating a relationship between the
volumes of these Einstein spaces and the number of holomorphic polynomials
(which correspond to chiral primary operators in the field theory dual) on the
corresponding affine cone.Comment: 25 pp, LaTeX, 1 figure, v2: refs adde