Geometry

Question Analysis  
This question involves similar solids and their volume ratios.
The main focus is on applying the relationship between the scale factor of similar figures and the ratio of their volumes.  

Key Concept Explanation  
For similar solids, if the scale factor (ratio of corresponding linear dimensions, e.g., height, radius) is , then the ratio of their volumes is .  
Let the smaller cone be Cone 1 (volume ) and the larger cone be Cone 2 (volume ).  

Step-by-Step Solution  
1. Find the scale factor for volumes:  
   
  (Here, is the ratio of the smaller cone’s linear dimensions to the larger cone’s linear dimensions.)  
2. Relate the heights using the scale factor:  
  Let inches (height of smaller cone) and be the height of the larger cone.  
  Since

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