Geometry

Question Analysis
This question involves similar rectangular pyramids and uses the given volume ratio to find the height of the larger pyramid.
The main focus is working backward from the volume ratio to find the scale factor (ratio of corresponding linear dimensions) and then using it to determine the unknown height.

Key Concept Explanation
For similar rectangular pyramids, if the ratio of their volumes is , then the ratio of their corresponding linear dimensions (such as height) is the cube - root of the volume ratio.
That is, if , then the ratio of corresponding linear dimensions is .

Step-by-Step Solution
Let the volume ratio of the two rectangular pyramids be , the height of the smaller pyramid be cm, and the height of the larger pyramid be .
First, find the ratio of the corresponding linear dimensions.
Since

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