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 `a.` Then its volume is `V=a^3` and the surface area is `A=6a^2` (a cube has six faces, each is a square with the side length `a`).

Therefore the ratio in question is

`A/V=(6a^2)/(a^3)=6/a.`

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

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