Problema Solution
Wire is often sold in pound spools according to the wire gauge number. that number refers to the diameter of the wire. How many meters are in a 10-lb spool of 12-gauge aluminum wire? A 12-gauge wire has a diameter of 0.0808 in. Aluminum has a density of 2.70 g/cm3
Answer provided by our tutors
So, this is a question simply requiring unit conversions. The length of the wire is simply solved by dividing the weight of the wire (10-lb) by density times volume.
Let 'w' represent the weight, let 'c' represent the cross-area of the wire, let 'd' represent the density and let 'l' represent the length of the wire.
w = cdl
solve for the unknown 'l':
l = w/(cd)
We want to convert density from g/cm^3 to lb/m^3 and convert cross-area from inches to meters. The cross-area would be "PI r squared", where 'PI' is substituted to signify the radical 'pi':
PI*r^2
We will use these conversions:
1 centimeter = 10^(-2) meters
1 inch = 0.0254 meters
1 gram = 0.00220462 pounds
So 'c' is:
(PI*(0.0404*0.0254)^2)
and 'd' is:
(2.70*(0.00220462)/(10^-6))
Applying the conversions to the basic equation [l = w/(cd)]:
l = 10/((PI*(0.0404*0.0254)^2)*(2.70*(0.00220462)/(10^-6)))
To numerically obtain a length:
l=507.83
So the length of the 10-lb wire is approximately 508 meters.