he 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

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 will set this up for you and you can do the calculations.

 

What you seek is the quantity h in the volume formula.

 

You are given density ρ and mass m, although you should convert units so that everything is in the same system of units.  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)]

 

You should be able to finish from here.  Just plug in the numbers after converting units as needed, which you should already know how to do.  Be careful with the units.