Geometry

Question Analysis
This question involves the similarity of cones and focuses on using the ratio of corresponding linear dimensions (radii) to find the volume of the larger cone given the volume of the smaller one.
The main focus is applying the concept that the ratio of the volumes of two similar solids is the cube of the ratio of their corresponding linear dimensions.

Key Concept Explanation
For two similar cones, if the ratio of a corresponding linear dimension (such as radius) is , then the ratio of their volumes .
This is because the volume formula of a cone , and in similar cones, the radius and height change proportionally.

Step-by-Step Solution
Let the ratio of the radii of the two cones be , the volume of the small cone cubic units, and the volume of the large cone be .
We know that .
Substitute the values:

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