Question

The surface area of a rectangular prism is increased by a factor of 16.

By what factor is the volume of the figure increased?
HH!

Answer 1

`64`

Explanation:

It was given that, the surface area of a rectangular prism is increased by a factor of 16.

Let k be the scale factor:

`{k}^(2) = 16`

`\implies \: k = √(16) = 4`

To determine the factor by which the volume of the figure is increased,we cube the scale factor to get:

`{k}^(3) = {4}^(3) = 64`

Therefore the volume is increased by a factor of 64