Suppose we have two convex bodies $A$ and $B$, where $A \subseteq B$.  Is it always true that $\mathrm{Vol}(A)/\mathrm{SurfaceArea}(A) \leq \mathrm{Vol}(B)/\mathrm{SurfaceArea}(B)$?It's true in all the examples I've tried, but I'm not sure how to prove the general case, or whether the general case is even true.
Do nested convex bodies have increasing Volume/Surface Area ratios?
convex optimization;convex geometry;high dimensional geometry