length of wire

Question

The gauge number of a wire is related to the diameter of the wire. Suppose you have a
10.0-lb spool of 12-gauge aluminum wire (diameter 0.0808 in). Calculate the length of
wire (in meters) on the spool. Assume that the wire is a cylinder (V = πr2
l, where V is the
volume, r is the radius, and l is the length.

Answer 1

CONVERT TO SI

1 lb = 453.6 g

1 in = 2.54 cm

mass: 10 lb x 453.6 g/lb = 4536 g

radius: r = (0.0808/2) = 0.0404 in

0.0404 in x 2.54 in/cm = 0.1026 cm

FIND VOLUME FROM DENSITY

V = (m/p)

4536/2.70 =1,680 cm³

SOLVE FOR LENGTH

1 m = 100 cm

l = (V/πr²)

1680/π(0.1026²) = 5.07 x 10⁴ cm

CONVER TO METERS

5.07 x 10⁴ cm = 507 m is the length of the wire spool