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…

Question

asked Oct 11, 2021 49.0k views

1 Answer

Diving · Answer 1 · 2021-10-15T03:00:56+0000

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