If the surface area of a cube is increased by a factor of 2, by what factor does the volume per unit area of surface of the cube change?

Step-by-step explanation:

The surface of a cube is defined as

Where is the length of a side.

If the surface is increased by a factor of 2, it would be

That is, each side would be double after such transformation. So, the surface of the increased cube is

Now, the initial volume of the cube is

After the increase, it would be

So, the increased volume is

Now, to find changing factor of the volume per unit area of surface, we have first have to notice the change in the area of the surface and its volume.

If you observe, the surface changed by a factor of 2, and the volume changed by a factor of 8. If we divide this

This means that the change of volume per unit area of surface is 4.