Geometry

Question Analysis
This question focuses on the similarity of rectangular prisms 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, where the ratio of volumes is equal to the cube of the ratio of corresponding linear dimensions.

Key Concept Explanation
For two similar rectangular prisms, if the ratio of their heights (or any corresponding linear dimension) is , the ratio of their volumes .
This is because the volume of a rectangular prism , and in similar prisms, all linear dimensions change in the same proportion.

Step-by-Step Solution
Let the height ratio of the two rectangular prisms be , and the volume of the smaller prism cubic inches, and the volume of the larger prism be .
We know that