Here's a chance for you to practice your dusty trigonometry skills and appear on the nationally syndicated radio show, Car Talk with Click and Clack. A listener called in and asked if there was a way that he could figure out when his cylindrical gas tank (the cylinder is on its side, not standing up) is a quarter full, since his gas gauge is broken. The hosts (who went to MIT) tried their hand at the problem but gave up, saying that the guy should just find someone else whose gas gauge isn't broken and measure how deep the gas is in that guy's tank when the gauge reads a quarter. According to Almea, a bunch of listeners called in and said you need calculus to calculate where the quarter mark on the gas tank would be.

Now, you don't need calculus to solve the problem, or at least I didn't. I solved it both with calculus and without. But both times I ended up with a hideous trigonometric mess that I was unable to turn into something nice. With Mathematica or another math computer program, I would be able to just plug in my mess and have it spit out an answer. Alas, I don't have Mathematica. This is vexing because the answer should vary simply with respect to the radius of the cylinder. If anyone has a spare few minutes, give it a whirl. (If the problem is unclear to you, let me know and I'll try to explain it better.)