Geometry

Question Analysis
This question involves the similarity of square - based pyramids and uses the ratio of the side lengths of their bases to find the volume of the smaller pyramid given the volume of the larger one.
The main focus is applying the volume - ratio formula for similar solids, where the ratio of volumes is the cube of the ratio of corresponding linear dimensions.

Key Concept Explanation
For similar square - based pyramids, if the ratio of the side lengths of their bases (a corresponding linear dimension) is , then the ratio of their volumes .
This is because the volume of a square - based pyramid , and in similar pyramids, all linear dimensions scale proportionally.

Step-by-Step Solution
Let the side length of the base of the smaller pyramid be inches, the side length of the base of the larger pyramid be inches, the volume of the larger pyramid be cubic inches, and the volume of the smaller pyramid be

Click "Show Answer" to reveal the answer and analysis