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:

$10\cdot\frac{3}{7}=\frac{30}{7}\text{ inches}$

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

$V=a^3$

Substituting:

$V=\left(\frac{30}{7}\text{ inches}\right)^3=\frac{30^3}{7^3}\text{ inches}^3$

Calculating and rounding to the nearest tenth:

V = 78.7 cubic inches