# Problem of the Day: 1/17/13

A frustum is a cone with its pointed end cut off, leaving two parallel faces. In this case, a cone of height 10 cm and radius 2 cm is made into a frustum of height 5 cm. What is the volume of this frustum?

Solution to yesterday’s problem:

You could solve this problem using proportions, but it would be much simpler and faster to calculate the answer mentally. If the ratio is $\frac{5}{6}$, then we should start thinking of multiples of these numbers whose difference is two. The first one we come across is 10 and 12. They fit the ratio, and 12 is two more than 10, so Lauren must be 10 years old.