a 16-gauge wire has a diameter of 0.05082 in. what length of wire in meters is found in a 1.60 lb spool of 16-gauge copper wire. density of copper is s 8.92g/cm^3

Answer 1

Let's first convert the diameter into cm and the mass into grams. There are 2.54 cm per inch and there 0.00220462 lb in 1 gram so:

Mass (m) equals density (ρ) times volume (V) or:

m = ρV

Volume (V) of a cylinder (wire is the shape of a very long skinny cylinder) is pi times radius (r) squared time the height or, in this case, length (L) so:

V = πr²L

And radius is diameter (d) divided by 2 or

r = d/2

So V = π(d/2)²L and plugging this into the mass equation:

m = ρπ(d/2)²L

Solving that equation for L we get:

L = m/(ρπ(d/2)²) = 725.7486551/(8.92π(0.1290828/2)²) = 6217.198745 cm

Since there is 1 meter in 100 cm we divide the answer by 100 to get meters.And since there are 3 significant figures in the givens, we also round to 3 sig figs giving us 62.2 meters