Question

A prism with a volume of 250 ft^3 is dilated by a factor of 3.The volume of the dilated prism is ____ ft^3.

Answer 1

In a volume the dilation makes the efect of increasing the volume by a factor of:

$k^3$

where k is the scale factor of the diltation.

In this case this means that the new volume will be:

$V^{\prime}=(3)^3(250)=27\cdot250=6750$

Therefore the volume of the dilated prism is 6750 cubic feet.