length of 12 gauge copper wire

Question

solid 12 gauge copper wire is essentially just a very long cylinder of copper.It is used extensively in house wiring.12 gauge wire has a diameter of .2052 cm.Copper has a density of 8.96 g/cm^3.What length of 12 gauge copper wire can be made from 1 kg of copper(1000g)?

Answer 1

Let us first use the density to find the volume of 1000 g of wire.

1000 g x 1 cm³/g = 1000 cm³

Now that we know the volume of the wire, and if we consider the wire to be a perfect cylinder, and we assume that the density of the copper is the same as the density of the wire, we can calculate the height of this cylinder using V = π r² h

V = volume = 1000 cm³

π = 3.1416

r = radius = diameter/2 = 0.2052 cm/2 = 0.1026 cm

h = height = ? = length

h = V/π r²

h = (1000 cm³) / (3.1416)(0.1026 cm)² = 1000 cm³ / 0.03307 cm²

h = 30,239 cm = 30,200 cm (to 3 significant figures) = 302 meters (to 3 significant figures)

(NOTE: The assumption that the density of copper = density of the wire assumes that the internal volume of the wire is negligible compared to the volume of the rest of the wire).