What is the ratio of the volume of a cube with edge length six inches to the volume of a cube with edge length one foot? Express your answer as a common fraction.
Hey, I remember this! The volume of a cube is just the length of one of its edges cubed! Right, so the volume of the first cube is just $6^3 = 216$ cubic inches. But wait, we need to express the volume of the second cube in inches as well. That's right, since one foot is equal to 12 inches we just need to cube 12 to find the volume of that cube. But I think we should simplify the ratio before we present our answer. That's a good idea. The ratio of the two volumes is just $\frac{216}{12^3}$. But $12^3 = 12 * 12 * 12 = 12 * 144 = 1728$. So the final ratio is just $\frac{216}{1728}$. And that simplifies to $\frac{1}{8}$. Yep. So $\frac{216}{12^3}=\frac{1}{8}$. And that's our answer.

