A cone is cut by a plane that runs parallel to its base, creating a smaller cone that is similar to the original cone. If the height of this smaller cone is one-third that of the original cone, what is the ratio of their volumes?
Show answer & explanation
Correct answer: C
Explanation
Height of the smaller cone = (1/3)H
Ratio of the volumes of similar solids = (Linear ratio)³
Linear ratio = 1 : 3
Ratio of volumes = (1/3)³ = 1 : 27