Geometry

Question Analysis
This question focuses on the relationship between the edge - length ratio of similar cubes and their surface areas.
The main focus is applying the principle that the ratio of surface areas of similar solids is the square of the ratio of their corresponding linear dimensions.

Key Concept Explanation
For two similar solids with a scale factor , the ratio of their surface areas and is .
In the case of cubes, the edge - length ratio serves as the scale factor, and since surface area is two - dimensional, it scales with the square of this factor.

Step - by - Step Solution
Let the scale factor be , , and