How many meters are in a 10-lb spool of 12-gauge aluminum wire? A 12-gauge wire has a diameter of 0.0808 inches and aluminum has a density of 2.70 g/cm^3

Question

The complete question is 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 inches and aluminum has a density of 2.70 g/cm^3 Solution with explanation please. TIA!

Answer 1

10lb=4540g approx. 1in=2.54cm approx. 0.0808 in=0.2052cm approx. Radius of wire=0.1026cm. Cross-sectional area of wire=π(0.1026)²=0.03308sq cm approx.

Density=mass/volume, volume=0.03308x cc, where x is the length in cm.

Mass=4540g, so density 2.70=4540/0.03308x, and x=4540/(2.70×0.03308)=50829cm=50829/100=508.29m.