Question 982924
i have a 20.5" cylinder (core) and I need to put 1800' of material on the outside of it.  the material is .022 thick.  what would the diameter be of the material after it has all of the material on it?
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If the 20.5" is the diameter:
The 1st turn adds 0.044 to the diameter.
The length of the 1st turn = pi*d = 20.5*pi =~ 64.4 inches
Each turn adds 0.044 to the ID --> adds 0.13823 to the circumference.
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For n turns,
Length = 20.5*pi + pi*(20.5 + n*0.044)*n
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1800' = 21600 inches
21600 = 20.5pi + 20.5*n*pi + 0.044n^2
0.044n^2 + 20.5*pi*n + (20.5pi - 21600) = 0
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--> 0.044n^2 + 64.4n - 21535.6 = 0
*[invoke solve_quadratic_equation 0.044,64.4,-21535.6]
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Ignore the negative solution
n =~ 281 turns
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dia with 281 turns = 20.5 + 281*0.044
dia = 32.82 inches
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I'll do the general case later.