__Category__: Solid Geometry"Published in Vacaville, California, USA"

One cube has a face equivalent to the total area of another cube. Find the ratio of their volumes.

__Solution__:

To illustrate the problem, it is better to draw the figure as follows

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Let B = be the area of a base of a large cube

x = be the length of the edge of a large cube

T = be the total area of a small cube

y = be the length of the edge of a small cube

V

_{1}= be the volume of a large cube

V

_{2}= be the volume of a small cube

The area of a base of a large cube is

The total area of a small cube is

From the given problem statement, we know that

The volume of a large cube is

The volume of a small cube is

Therefore, the ratio of their volumes is