A Truck, a Box, and More Than 8th Grade Mathematics!

Sep 14, 2020

RAY: This is from my lower mathematics series. This was sent in by an anonymous physicist who clearly doesn't want any of his colleagues to know that he listens to Car Talk. He writes:

Some time ago you entertained a caller who wanted to know how to measure the fuel level in the cylindrical tank of his diesel truck. These tanks are cylinders that lie on their side and the filler is on the top. Specifically, he wanted to know if he inserted a broomstick through the tank's filler opening, where on the stick should he put the ¼ full mark?

His tank was 20-inches in diameter. While he knew that the half-full mark was at 10 inches, he was doubtful that the 1/4 full mark was at 5 inches. You, two bozos, agreed with him and after fumbling around for a few minutes, determined it would take more than the 8th-grade mathematics at your disposal to figure out the answer.

Well, a few weeks ago, my wife and I were traveling from DC to Wilmington, North Carolina, by car. While stopped at a roadside diner, I told her the story of your mathematical misadventure. I noticed a fellow a few stools down listening intently. After a while, he interrupted us and said, “I happen to be a diesel truck driver myself and while I don't know the answer, I think I might have something in my truck that can help figure out the answer.”

"'You do?”

''Yeah. It's something that came with last night's dinner,” he said. With that, he sprang from his seat and two minutes later, returned with a rather large box in his hands. He then produced a jackknife from his belt, asked our waitress for a pencil, and with a surgeon's precision, he got to work.

The question is what did he do to determine where the mark should be on the stick to signify the ¼ full mark on the tank?


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