Tricky Integration Problem
At my job we deal with "steel coils". These are huge roles of sheet metal that can weigh up to 30+ tons. Think giant paper towel roll made of steel. An interesting question I had, but cannot seem to mathematically figure out on my own is the following: Given a coil with exterior diameter of 1000mm, interior diameter of 250mm, and a metal thickness of 2.5mm, how long will the sheet of metal be if you unroll it completely? The answer, according to an online calculator I found it 294.52 meters. I know that to figure this out, I'll need to integrate the various layers of the coil, but I can't seem to figure out the right set-up. Can anyone help?
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