Geometry

Question Analysis
This question involves the concept of similarity in three - dimensional figures and the relationship between the scale factor and the surface areas of similar solids.
The main focus is on applying the principle that the ratio of the surface areas of two similar solids is equal to the square of the ratio of their corresponding linear dimensions (scale factor).

Key Concept Explanation
For two similar solids with a scale factor , the ratio of their surface areas and is given by .
This is because surface area is a two - dimensional measurement, and when the linear dimensions are scaled, the surface area scales by the square of the scale factor.

Step - by - Step Solution
Let the scale factor of the two prisms be and , and let square inches be the surface area of the smaller prism and be the surface area of the larger prism.
We know that , so

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