A cube of volume 1000 units3 is dilated by a scale factor of 1/2. What is the volume of the image? (Hint: Determine the side length of the pre-image first.)

Question

Possible answers below:

10 units³ 

125 units³

500 units³

8000 units³

Answer 1

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

(1/2)² = 1/8

1/8 of 1000 is 125

Answer 2

Hi. It would appear to me to be 125 units. If the actual cube has a volume of 1000, it would be based on length x width x height, or 10x10x10 (=1000). Therefore, if we are to dilate by 1/2 for the image, we would multiply half those sizes, or 5x5x5 (=125).