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Q&A How to calculate remaining volume of a wire spool

posted 2y ago by re89j‭  ·  edited 2y ago by re89j‭

Answer
#3: Post edited by user avatar re89j‭ · 2022-10-07T02:38:25Z (about 2 years ago)
  • After I wrote up the question, I think the answer just hit me.
  • Calculate the area of three circles: (was going to say cylindars, but I don't think that axis matters)
  • a) the minimum/empty diameter
  • b) the maximum/full diameter
  • c) the current media diameter
  • Then:
  • b-a = the starting area of media
  • c-a = current area of media
  • current area / starting area = % remaining.
  • For an 8 inch diameter spool with a 4 inch core:
  • ![graph showing material remaining for given empthy depth](https://math.codidact.com/uploads/hTXyQhYDNmBdcevgCpYJpwdS)
  • After I wrote up the question, I think the answer just hit me.
  • Calculate the area of three circles: (was going to say cylindars, but I don't think that axis matters)
  • a) the minimum/empty diameter
  • b) the maximum/full diameter
  • c) the current media diameter
  • Then:
  • b-a = the starting area of media
  • c-a = current area of media
  • current area / starting area = % remaining.
  • For an 8 inch diameter spool with a 4 inch core:
  • ![graph showing material remaining for given empthy depth](https://math.codidact.com/uploads/hTXyQhYDNmBdcevgCpYJpwdS)
  • The smaller the core, the more pronounced the curve. If the core is 1000 inches, then it looks almost straight, as I'd expect.
#2: Post edited by user avatar re89j‭ · 2022-10-07T02:36:54Z (about 2 years ago)
Added Graph
  • After I wrote up the question, I think the answer just hit me.
  • Calculate the area of three circles: (was going to say cylindars, but I don't think that axis matters)
  • a) the minimum/empty diameter
  • b) the maximum/full diameter
  • c) the current media diameter
  • Then:
  • b-a = the starting area of media
  • c-a = current area of media
  • current area / starting area = % remaining.
  • After I wrote up the question, I think the answer just hit me.
  • Calculate the area of three circles: (was going to say cylindars, but I don't think that axis matters)
  • a) the minimum/empty diameter
  • b) the maximum/full diameter
  • c) the current media diameter
  • Then:
  • b-a = the starting area of media
  • c-a = current area of media
  • current area / starting area = % remaining.
  • For an 8 inch diameter spool with a 4 inch core:
  • ![graph showing material remaining for given empthy depth](https://math.codidact.com/uploads/hTXyQhYDNmBdcevgCpYJpwdS)
#1: Initial revision by user avatar re89j‭ · 2022-10-06T23:55:54Z (about 2 years ago)
After I wrote up the question, I think the answer just hit me.

Calculate the area of three circles: (was going to say cylindars, but I don't think that axis matters)
a) the minimum/empty diameter
b) the maximum/full diameter
c) the current media diameter

Then:
b-a = the starting area of media
c-a = current area of media

current area / starting area = % remaining.