Geometry

Question Analysis
This question combines the concepts of volume and surface area of similar rectangular prisms.
The main focus is using the volume ratio to find the scale factor, and then using the scale factor to determine the surface area of the larger prism, as the ratio of the surface areas of two similar solids is the square of the scale factor.

Key Concept Explanation
If the ratio of the volumes of two similar solids is , then the scale factor of their corresponding linear dimensions is .
The ratio of their surface areas . This is because surface - area calculations involve the square of the linear dimensions of the solid.

Step-by-Step Solution
Since the volume ratio of the two rectangular prisms is , we can find the scale factor. As and , the scale factor of the corresponding linear dimensions is .
Let the surface area of the smaller prism be square units and the surface area of the larger prism be .
The ratio of the surface areas is

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