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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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| Photo by Math Principles in Everyday Life |
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
V1 = be the volume of a large cube
V2 = 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
