If the length of the side of a cube increases, what happens to the surface area to volume ratio?

Hello!

Denote the length of a cube side as Then its volume is and the surface area is (a cube has six faces, each is a square with the side length ).

Therefore the ratio in question is

As we see from this formula, the ratio decreases when side length increases (and vice versa).

This behaviour is common for all similar three-dimensional bodies.