Question

For each of the following, find the percent change in the volume of a cube. The length of the side of the cube was first increased by 50% and then decreased by 20%.

Answer 1

the volume increased by 72.8%

Explanation:

After the dilations, the scale factor for the length of the side is ...

(1 +50%)·(1 -20%) = 1.50·0.80 = 1.20

The scale factor for volume is the cube of this: 1.20^3 = 1.728

This represents an increase over the original volume of 1 by ...

1.728 -1 = 0.728 = 72.8%

The change in the volume of the cube is an increase of 72.8%.