Geometry

Question Analysis
This question combines the concept of the ratio of surface areas of similar cylinders with the relationship between the radius and the surface - area formula.
The main focus is on using the surface - area ratio to find the scale factor and then applying it to the radius.

Key Concept Explanation
Since the ratio of the surface areas of two similar solids is the square of the scale factor , we first find the scale factor from the given surface - area ratio.
For similar cylinders, the ratio of corresponding linear dimensions (such as radius) is equal to the scale factor.

Step - by - Step Solution
Let the scale factor be , and .
Then , where

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