The volume of a cone is 54 pi cubic inches. The radius and height of the cone are both reduced by a factor of 3 to create a new cone. What is the volume of the new cone?

Question

Is the volume of the new cone 18pi cu in

A. 2 pi cu inches
B. 6 pi cu inches
C. 9 pi cu inches
D. 18 pi cu inches

Answer 1

The volumes of similar cones (i.e. all linear dimensions are proportional) are proportional to the cube of the linear ratios.

For example, if a cone has twice the linear dimensions of a similar cone, the volume is 2³=8 times the similar cone.