Question

If the surface area of a cube is increased by a factor of 2 (so that the new surface area is twice the size of the original surface area), by what factor does the volume of the cube change?

Answer 1

Answer:2.828

Step-by-step explanation:

Given

Surface area of a cube is increased by a factor of 2

Let the original surface area be A

such that new surface area is 2A

for volume we need to know new radius

$6(a')^2=2\times 6r^2$

where r'=new radius

r=original radius

$a'=\sqrt{2}a$

New volume(V')$=(a')^3=(\sqrt{2}a)^3$

$V'=2\sqrt{2}a^3$

Original volume$=a^3$

$\frac{V'}{V}=\frac{2\sqrt{2}a^3}{a^3}$

$V'=2\sqrt{2}V=2.828V$