Geometry

Question Analysis
This question focuses on using the ratio of surface areas of similar cones to find the slant height of the larger cone.
The main focus is on understanding the relationship between the scale factor and the ratio of surface areas, and applying it to a specific linear dimension (slant height) of the cones.

Key Concept Explanation
For two similar solids, the ratio of their surface areas is equal to the square of the scale factor .
We can find the scale factor from the given surface - area ratio and then use it to find the slant height of the larger cone since the ratio of corresponding linear dimensions (like slant height) of similar solids is equal to the scale factor.

Step - by - Step Solution
Let the scale factor be , and .
Then , where is related to the smaller cone and