A cube with an original volume of 8 units3 has been dilated. What was the scale factor if the volume is now 64 units3? (Hint: Determine the side length of the pre-image first.)

Question

Possible answers:

2

4

8

16

Answer 1

The volumes of two similar figures are related as the cube of the scale factor

64 / 8 = s³

4³ / 2³ = s³

2³ = s³

2 = s

Answer 2

You have to find the side length of both cubes. To do this, take the cube root. This give the original cube has a side length of 2 and the dilated cube will have a side length of 4.

Therefore the scale factor is 4/2 = 2