Geometry

Question Analysis
This question focuses on the similarity of cylinders and uses the given volume ratio and the radius of the small cylinder along with the height of the large cylinder to find the height of the small cylinder.
The main focus is working backward from the volume ratio to find the scale factor and then using it to determine the unknown height.

Key Concept Explanation
For similar cylinders, if the ratio of their volumes is , then the ratio of their corresponding linear dimensions (such as radius or height) is .
Since the volume of a cylinder , and in similar cylinders, the radius and height change proportionally, we can use the volume ratio to find the relationship between the dimensions.

Step-by-Step Solution
Let the height of the large cylinder be cm, the volume of the small cylinder be , and the volume of the large cylinder be .
Given that

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