When Half is Not

Glasses shaped like cones and frustums don't behave nicely. The relationship between the level of the liquid in the glass and the percent that the glass is empty or full is complicated. Students solve a range of problems relating the dimensions of the glass to the state of the spaces inside it.

This is a layered problem that starts out with basic but interesting problems in a cone and then (for more advanced students) moves to problems within frustums. The algebra is challenging, but the results are very satisfying.