Geometry

Question Analysis
This question focuses on the relationship between the volume and radius of a sphere when the volume changes.
The main focus is on using the volume formula to establish how the change in volume affects the radius.

Key Concept Explanation
The volume formula for a sphere is .
If the new volume is related to the original volume by a factor (i.e., ), we can find the relationship between the new radius and the original radius by substituting into the volume formula.

Step-by-Step Solution
Let the original volume be and the new volume be .
Given that , we substitute the volume formulas:

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