Geometry

Question Analysis
This question deals with similar cylinders and focuses on using the ratio of their radii to find the volume of the larger cylinder given the volume of the smaller one.
The main point is applying the volume - ratio formula for similar solids, where the ratio of volumes is the cube of the ratio of corresponding linear dimensions.

Key Concept Explanation
For two similar cylinders, if the ratio of their radii (a corresponding linear dimension) is , the ratio of their volumes .
Since the volume of a cylinder , and in similar cylinders, the radius and height change proportionally, we can use the radius ratio to find the volume relationship.

Step-by-Step Solution
Let the radius 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

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