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June 25th, 2015, 12:38 PM   #1
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Circumference of part of a circle

Hi Guys

Hope this is in correct forum.

I have a roll of paper whose diameter is 50-inches and it weighs 4,000lbs (width is about 75-inches if it matters).

These are the only attributes I know.

I'm trying to figure out what the diameter would be if I used 3,000lbs (i.e. I've used 75% of the weight). It's wound on a core whose external diameter is about 6-inches (but I can ignore this if needed for simplicity).

I'm figuring there has to be a way to figure out the diameter remaining if the 75% is left, but I'm drawing a blank. (I added a diagram in the attached)


Can someone point me in right direction?

Thanks

Mark
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File Type: jpg AreaOfCircle.jpg (8.8 KB, 3 views)
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June 25th, 2015, 01:00 PM   #2
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Weight is proportional to volume. Volume of cylinder is proportional to $\displaystyle r^2$.

Roll of paper volume proportional to $\displaystyle 50^2-6^2=2464$.

Reduce volume proportional to .75x2464=1848.

Final diameter = $\displaystyle \sqrt{1848+36}=43.4$.
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June 26th, 2015, 03:44 AM   #3
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Thanks a lot Mathman!
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