I was looking at the following problem: if I have a "simple" convex (like a ball or a parallelotope for example) in $\mathbb R^n$ and I want to know what is the biggest (in volume) hyperplane section of this set.
I did find some formulas online about the cube, but I want to know more and how to prove these formulas.
So I'm looking for references on the volume of sections of convex bodies if you could advise me some of them.