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June 25th, 2015, 12:38 PM  #1 
Newbie Joined: Jun 2015 From: Chicago Posts: 2 Thanks: 0  Circumference of part of a circle
Hi Guys Hope this is in correct forum. I have a roll of paper whose diameter is 50inches and it weighs 4,000lbs (width is about 75inches 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 6inches (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 
June 25th, 2015, 01:00 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,704 Thanks: 669 
Weight is proportional to volume. Volume of cylinder is proportional to $\displaystyle r^2$. Roll of paper volume proportional to $\displaystyle 50^26^2=2464$. Reduce volume proportional to .75x2464=1848. Final diameter = $\displaystyle \sqrt{1848+36}=43.4$. 
June 26th, 2015, 03:44 AM  #3 
Newbie Joined: Jun 2015 From: Chicago Posts: 2 Thanks: 0 
Thanks a lot Mathman!


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circle, circumference, part 
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