Hard Geometry Question

Polyhedron "P" is inscribed in a sphere of radius 36 (meaning that all vertices of  lie on the sphere surface). What is the least upper bound on the ratio

$\frac{\text{volume of }P}{\text{surface area of }P}~?$

In other words, what is the smallest real number "t" such that:

$\frac{\text{volume of }P}{\text{surface area of }P} \le t$

must be true for all polyhedra that can be inscribed in a sphere of radius 36?