Hello, I am having problems with this geometry problem. Please help! Thanks.
Polyhedron \(P\) is inscribed in a sphere of radius \(36\) (meaning that all vertices of \(P\) 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 \(P\) that can be inscribed in a sphere of radius 36?
