An Honest to Goodness Real World Math Problem

I’ve got a degree in Electrical Engineering (U of Arizona, 1991, Go Cats!) which required me to take a bunch of math classes.  Darn near every semester I took a math class, starting with second semester Calculus because I AP’d out of the first semester (go me!). Calculus, Vector Calculus, partial differential equations, took it all.

Out here in the real world, I work as a Control Systems Engineer. Want to run a plant full of equipment? I do everything from design to installation to programming. None of that ordinarily takes partial differential equations, at least not that I’ve run into yet. Almost all the math I use I use in the programming phase doing conversions and other things. We live in a world where if I want to measure something, like water level, say, I pop on the internet, type in “water level”, and almost every single time some company is out there with an instrument already for sale that will do it. No need for me to design from scratch.

My point here is that my math muscles atrophy, but every now and then someone brings me a math problem, and I love it when they do. This one was geometry:

A worker here made a 500lb test weight from scratch, using 18 inch (diameter) metal pipe cut 12 inches tall. He sealed one end shut then stood the pipe on that end so he had a barrel. He then sealed the other end, but left a hole so that he could fill it with a material to add weight. He filled it until it weighed 500lb – it was nearly full.

So he came to me and said he wanted to make a 1000lb weight now, using 26 inch pipe. He needed to use the same filler material. How tall would it have to be?

Not partial differential equations, but still neat.

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