Geometry

Question Analysis
This question focuses on the similarity of triangular prisms and the relationship between their volumes based on the ratio of corresponding side lengths.
The main focus is applying the fundamental rule that for similar solids, the ratio of volumes is equal to the cube of the ratio of their corresponding linear dimensions.

Key Concept Explanation
For any two similar solids, if the scale factor (ratio of corresponding linear dimensions) is , then the ratio of their volumes .
This principle applies to triangular prisms, where changes in side lengths proportionally affect the overall volume.

Step-by-Step Solution
Let the side - length ratio of the two triangular prisms be , and the volume of the smaller prism cubic units, and the volume of the larger prism be .
We know that