Question

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?

Answer 1

what is the surface area of the first cube but you should multiply the first cube by the scale factor if it is an enlargement if it is a reduction you divide it by the scale factor

plz mark as brainlist

Answer 2

Answer:

4

Step-by-step explanation:

The surface of a cube is defined as

$S=6l$

Where $l$ is the length of a side.

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

$S=6(2l)$

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

$S=12l$

Now, the initial volume of the cube is

$V=l^{3}$

After the increase, it would be

$V=(2l)^{3}$

So, the increased volume is

$V=8l^{3}$

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

$\frac{8}{2} =4$

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