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mark-r | 1 month ago

I was able to do something similar by using gross approximations and conversions to/from metric. My coworker had just bought a surplus stainless steel water tank for solar heating, and was wondering how much it would weigh when full. It was cylindrical, so I asked him for the diameter and the height. In my head I converted those measurements to inches, then to centimeters by multiplying by 2.5. I divided the diameter by 2, squared it, and multiplied by 3 (close enough to pi) to get the area. Then I converted the area and the height to their nearest power of 2 so I could take advantage of logarithms. Multiplying the area and height was as easy as adding the exponents, which gave me cubic centimeters. The weight of water is almost by definition 1 gram per 1 cc. Divide by 1000 to get kg by subtracting 10 from the exponent, then multiply by 2 to get approximate pounds by adding 1 to the exponent. By the time he was done telling me the dimensions, I had an answer for him. It definitely wasn't correct, but all he needed was a ballpark anyway.

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