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

When the surface area of a cube is doubled, the volume of the cube will also double.

Step-by-step explanation:

To determine the factor by which the volume of a cube changes when its surface area is increased by a factor of 2, we can use the formula for the volume of a cube, which is V = s³, where s is the length of a side of the cube.

Let's assume the original cube has a side length of s. The original surface area of the cube is 6s². If the surface area is increased by a factor of 2, the new surface area would be 2 * 6s² = 12s².

Since the volume of the cube is directly proportional to the length of its side, when the surface area is doubled, the volume will also double. Therefore, the factor by which the volume of the cube changes is 2.

Answer 2

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* 6r^2`

where r'=new radius

r=original radius

`a'=√(2)a`

New volume(V')
`=(a')^3=(√(2)a)^3`

`V'=2√(2)a^3`

Original volume
`=a^3`

`(V')/(V)=(2√(2)a^3)/(a^3)`

`V'=2√(2)V=2.828V`