Geometry

Question Analysis
This question involves the concept of similar solid figures, specifically square pyramids, and focuses on the relationship between the volumes of similar solids.
The main focus is understanding that the ratio of the volumes of two similar solids is equal to the cube of the scale factor of their corresponding linear dimensions.

Key Concept Explanation
For two similar solids, if the scale factor of their corresponding side lengths (or any linear dimension) is , then the ratio of their volumes is .
This is a fundamental property of similar solid geometry.

Step-by-Step Solution
Let the scale factor of the two square pyramids be , the volume of the smaller pyramid be cubic inches, and the volume of the larger pyramid be .
We know that