"The calculus of the dipstick?!" Tom and Ray Magliozzi. Car Talk, 30 November 2002.
Car Talk is a hilarious NPR call-in show offering serious advice on car problems. One listener, a truck driver named Rich, called in with a broken gas gauge. He had a cylindrical gas tank, on its side on his truck, and had to measure his gas by putting a wooden dowel in the tank. He could use the height of the gas to determine when the tank was half full, but wanted to know what heights were associated with one-quarter full, or one-quarter empty. Tom and Ray initially thought it was an easy problem, but quickly realized that some non-trivial mathematics was needed so they appealed to their listeners. The problem and solutions are here. Rich's tank is 10 inches in radius. The tank is one-quarter full when the gas is a little less than six inches deep. The featured solution, using trigonometry, is from a page with solutions to some circle problems at Ask Dr. Math.
--- Mike Breen