Geometry

Question Analysis  
This question involves similar solids and their surface area/volume ratios.
The main focus is using the surface area ratio to find the scale factor, then applying it to determine the volume ratio.  
Key Concept Explanation  
For similar solids:  
1. The ratio of surface areas is the square of the scale factor ().  
2. The ratio of volumes is the cube of the scale factor ().  
Let the smaller sphere be Sphere 1 () and the larger sphere be Sphere 2 ().  

Step-by-Step Solution  
1. Find the scale factor from the surface area ratio:  
   
  Since surface area ratio , solve for :  
   
  (Here,

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