Geometry

Question Analysis
This question focuses on the concept of similar triangular prisms and the relationship between their volumes.
The main focus is applying the principle that for similar solids, the ratio of their volumes is equal to the cube of the scale factor of their corresponding linear dimensions.

Key Concept Explanation
For any two similar solids, when the scale factor of their corresponding linear measurements (such as edge lengths) is , the ratio of their volumes .
This rule applies to all similar three - dimensional shapes, including triangular prisms, and is crucial for solving volume - related problems involving similar solids.

Step-by-Step Solution
Let the scale factor of the two triangular prisms be , and the volume of the smaller prism cubic inches, and the volume of the larger prism be .
We know that

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