Geometry

Question Analysis
This question deals with similar square - based pyramids and focuses on using the ratio of their base - side lengths to find the volume of the smaller pyramid given the volume of the larger one.
The main point 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 their base - side lengths (a linear dimension) is , the ratio of their volumes .
The volume of a square - based pyramid , and in similar pyramids, all linear dimensions (base - side length, height) are in the same proportion.

Step-by-Step Solution
Let the base - side - length ratio of the two pyramids be , the volume of the larger pyramid cubic feet, and the volume of the smaller pyramid be .
We know that

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