Geometry

Question Analysis
This question focuses on the similarity of cylinders and the relationship between their volumes based on the ratio of their heights.
The main emphasis is on using the volume - ratio formula for similar solids, considering that for similar cylinders, the ratio of volumes is related to the cube of the ratio of their linear dimensions (height in this case, since the radius ratio is the same as the height ratio for similar cylinders).

Key Concept Explanation
For two similar cylinders, if the ratio of their heights (or any corresponding linear dimension) is , the ratio of their volumes .
This is because the volume of a cylinder , and when the cylinders are similar, the radius and height change in the same proportion.

Step-by-Step Solution
Let the height ratio of the two cylinders be , and the volume of the smaller cylinder cubic centimeters, and the volume of the larger cylinder be .
We know that

Click "Show Answer" to reveal the answer and analysis