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If a cube has an edge equal to the diagonal of another cube, find the ratio of their volumes.
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| Photo by Math Principles in Everyday Life |
Solution:
Consider the given figure above
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| Photo by Math Principles in Everyday Life |
Let V1 = be the volume of a small cube
y = be the edge of a small cube
V2 = be the volume of a big cube
x = be the edge of a big cube
For a small cube:
If the diagonal of a small cube is x, then the value of the edges, y will be equal to
Therefore, the volume of a small cube is
For a big cube:
The volume of a big cube is
Therefore, the ratio of their volumes is equal to
