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?
04
08
O 32
O 64

Answer 1

The volume of the prism increased by a factor of 64.

Explanation:

Given that the original prism and the increased prism are similar, we have that the scale factor is:

Area ∝ (length of side) x (length of side)

If the area increases by a factor of 16, each side increases by a scale factor of √16 = 4. Regarding the volume:

Volume ∝ (length of side) x (length of side) x (length of side)

Thus the increase factor for the volume, in this case, is 4 x 4 x 4 = 64.