SOLUTION: A cube has one face that is equal to the total surface area of another cube. Find the ratio of their volumes.

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Question 348614: A cube has one face that is equal to the total surface area of another cube. Find the ratio of their volumes.
Answer by nyc_function(2741) About Me  (Show Source):
You can put this solution on YOUR website!
Let the length of an edge on the smaller cube be x; then the total surface area

of the small cube is 6x^2 and its volume is x^3.


The large cube has one face with an area of 6x^2, so each edge is (sqrt6)x; the


volume of the large cube is (6sqrt6)x^3, and the ratio of their volumes is


6sqrt6: 1.