  We study the matrix models that result from localization of the partition
functions of N=2 Chern-Simons-matter theories on the three-sphere. A large
class of such theories are conjectured to be holographically dual to M-theory
on Sasaki-Einstein seven-manifolds. We study the M-theory limit (large N and
fixed Chern-Simons levels) of these matrix models for various examples, and
show that in this limit the free energy reproduces the expected AdS/CFT result
of N^{3/2}/Vol(Y)^{1/2}, where Vol(Y) is the volume of the corresponding
Sasaki-Einstein metric. More generally we conjecture a relation between the
large N limit of the partition function, interpreted as a function of trial
R-charges, and the volumes of Sasakian metrics on links of Calabi-Yau four-fold
singularities. We verify this conjecture for a family of U(N)^2 Chern-Simons
quivers based on M2 branes at hypersurface singularities, and for a U(N)^3
theory based on M2 branes at a toric singularity.
