Question

6. The ratio of the lengths of the sides of twocubes is 3: 7. The larger cube has an edgelength of 10 inches. What is the volume of thesmaller cube rounded to the nearest tenth?

Answer 1

The ratio of the lengths of the sides of the cubes is 3:7.

If the larger cube has an edge length of 10 inches, the other (smaller) cube has an edge length of:

`10\cdot(3)/(7)=(30)/(7)\text{ inches}`

The volume of a cube is the cube of its edge length:

`V=a^3`

Substituting:

`V=\left((30)/(7)\text{ inches}\right)^3=(30^3)/(7^3)\text{ inches}^3`

Calculating and rounding to the nearest tenth:

V = 78.7 cubic inches