he diameter of metal wire is often referred to by its American wire gauge number.

Question

The diameter of metal wire is often referred to by its American wire gauge number. A 16-gauge wire has a diameter of 0.05082 inches. What length of wire, in meters, is there in a 1.00 pound spool of 16-gauge copper wire? The density of copper is 8.92 g/cm3. (There are 2.2 pounds per kilogram. The volume of a cylinder is found by using the formula V = r2h).

Answer 1

I gave you the steps to solving this problem in your previous posting.  Just convert units and plug in the numbers.

You are given density ρ and mass m. Get volume from

V = m/ρ

But since

V = πr²h = πd²h/4,

(where d is the diameter, which you get from the gauge of the wire), you can combine the 2 equations above and get

h = [4 / (πd²)] V = [4 / (πd²)] (m/ρ)]

Final equation for h:

h = [4 / (πd²)] (m/ρ)]

At this point, all you have left to solve is an elementary arithmetic problem.  Just plug in the numbers in appropriate units.