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

If a cube has an edge equal to the diagonal of another cube, find the ratio of their volumes.

Photo by Math Principles in Everyday Life |

__Solution__:

Consider the given figure above

Photo by Math Principles in Everyday Life |

Let V

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

y = be the edge of a small cube

V

_{2}= 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