  We present some formulae for the moments of inertia of homogeneous solids of
revolution in terms of the functions that generate the solids. The development
of these expressions exploits the cylindrical symmetry of these objects, and
avoids the explicit use of multiple integration, providing an easy and
pedagogical approach. The explicit use of the functions that generate the solid
gives the possibility of writing the moment of inertia as a functional, which
in turn allows us to utilize the calculus of variations to obtain a new insight
into some properties of this fundamental quantity. In particular, minimization
of moments of inertia under certain restrictions is possible by using
variational methods.
