  We show that the Reeb vector, and hence in particular the volume, of a
Sasaki-Einstein metric on the base of a toric Calabi-Yau cone of complex
dimension n may be computed by minimising a function Z on R^n which depends
only on the toric data that defines the singularity. In this way one can
extract certain geometric information for a toric Sasaki-Einstein manifold
without finding the metric explicitly. For complex dimension n=3 the Reeb
vector and the volume correspond to the R-symmetry and the a central charge of
the AdS/CFT dual superconformal field theory, respectively. We therefore
interpret this extremal problem as the geometric dual of a-maximisation. We
illustrate our results with some examples, including the Y^{p,q} singularities
and the complex cone over the second del Pezzo surface.
