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Carpedium

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I have a real world application that I need some help with. I am sensitive to the fact that this is not the space for homework questions, or homework style questions. I feel that this is neither. If you disagree, please let me know and I will post it elsewhere.

It has been a while since college, any help would be appreciated. I believe that this is an integral calculus problem. The reel spool diameter changes as line is wound on the reel. I have posted this on other math forums and have not received input.

I have a fishing reel that has a line counter on it. As you reel in or let line out, it counts the number of revolutions of the spool and mechanically translates it into feet. The line counter is designed such that it is only accurate when the spool is full of line.

When the reel is empty, one foot on the line counter equals four inches of line on the spool. The spool is 0.5 inches in diameter with no line.

The reel is capable of holding 310 yards of line that is 0.019" in diameter, or 3.164 cubic inches of line.

The line that I intend to use is 0.0157 inches in diameter.

I have three reels and I want to fill each with 1000 feet line from a 1000 yard spool.

The problem:

Need to calculate the ending line counter reading when 1000 feet of line has been spooled up on the reel from empty.

Thank you in advance for your help.