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:
[tex]10\cdot\frac{3}{7}=\frac{30}{7}\text{ inches}[/tex]The volume of a cube is the cube of its edge length:
[tex]V=a^3[/tex]Substituting:
[tex]V=\left(\frac{30}{7}\text{ inches}\right)^3=\frac{30^3}{7^3}\text{ inches}^3[/tex]Calculating and rounding to the nearest tenth:
V = 78.7 cubic inches
