Geometry

Question Analysis
This question involves multiple similar rectangular prisms and focuses on using the ratio of their heights to find the volumes of each prism and then calculate the combined volume.
The main focus is applying the concept that the ratio of volumes of similar solids is the cube of the ratio of their corresponding linear dimensions, and then performing a cumulative volume calculation.

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

Step-by-Step Solution
Let the ratio of the heights of the three prisms be , and the volume of the smallest prism cubic feet.
Since and , then .
Substituting

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