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:

solve for 'l'

l=507.83


So the length of the 10-lb wire is approximately 508 meters.