Geometry

Question Analysis
This question focuses on the similarity of frustums of cones and the relationship between their volumes based on the ratio of their heights.
The main focus is applying the principle that for similar solids, the ratio of their volumes is equal to the cube of the ratio of their corresponding linear dimensions. Here, the relevant linear dimension is the height.

Key Concept Explanation
For two similar frustums of cones, if the ratio of their corresponding linear dimensions (such as height) is , then the ratio of their volumes .
This concept is derived from the general property of similar solids, where all linear measurements scale proportionally, and the volume, being a three - dimensional quantity, is affected by the cube of this scale factor.

Step-by-Step Solution
Let the height of the smaller frustum be cm, the height of the larger frustum be cm, the volume of the smaller frustum be cubic cm, and the volume of the larger frustum be .
First, find the ratio of the heights:

Click "Show Answer" to reveal the answer and analysis