Question

ACION

A student claims that if you dilate the net for a cube using a scale factor of 2, the surface



area of the resulting cube is multiplied by 4 and the volume is multiplied by 8. Does this



claim make sense?



(select)



make sense.

Answer 1

Answer:Yes

Explanation:

Given

Suppose side length of cube is a

If we dilate the cube using a scale factor of 2

Side length becomes 2a

and the surface area becomes
`=6(\text{side length})^2`

Surface area
`=6(2a)^2`

Surface area
`=4* 6(a)^2`

Thus surface area multiplied by a factor of 4

Now for volume

`V=(\text{side length })^3`

`V=(2a)^3`

`V=8(a^3)`

Therefore volume is multiplied by a factor of 8

Therefore the above statements make sense