How Do You Convert the Volume of a 16-Gauge Wire into Its Length?

[kevinnn]

Homework Statement

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 in.
What length of wire, in meters, is found in a 1.00-lb spool of 16-gauge copper wire? The density of copper is 8.92g/cm3.

Homework Equations

The Attempt at a Solution

I just can't get the last step. I currently have it set up as,

(1lb)x(453.592g/1lb)x(1cm^3/8.92g)x(1in^3/16.387cm^3)x... I know I need to get from inches cubed to meters. But how do I go from something cubic to linear? Thanks for the time!

 

[SteamKing]

How would you go from cubic centimeters to cubic meters? How many inches are in 1 meter?

 

[kevinnn]

100 inches in one meter. I can't take the cube root of both though so that's where I get stuck.

 

[Enigman]

100 inches in one meter. I can't take the cube root of both though so that's where I get stuck.

WHAT?!? 100cm not inch = 1 m

 

[symbolipoint]

Cubic, just means the conversion occurs as a factor three times, so the conversion ratio for the unit must also be done three times.

 

[vela]

You need to use the information given about the diameter of the wire. If the diameter of the wire were increased, the length of the wire would be decreased, right? Why exactly? What's the relationship between the diameter and the length? If you figure that out, it should be pretty clear about what you need to do to get from a volume to a length.

 

[Chestermiller]

Start by calculating the cross sectional area of the wire. How is the volume of the wire (i.e., cylinder) related to the cross sectional area and the length? If you know the volume of the wire and the density of the material comprising the wire, how do you calculate the mass of material?

 

[kevinnn]

Ok well I have the formula of a cyllinder (v=(PI)r^2h). The volume is related to the length through the variable h. I will work through the problem when I get home to see if I can solve it now.

 

[kevinnn]

I still got the wrong answer. What I did is I calculated the volume of wire I have,
1.00lb*(453.592g/1lb)*(1cm^3/8.92g)=50.9 cubic centimeters. I then used the equation for the volume of a cylinder and set it up like this. 50.9=(pi)(0.05082in)^2(h) and solved for h. The value I get is way too large.

 

[vela]

Make sure you're using the radius and have the correct units.

 

[kevinnn]

ohh thank you. That was a dumb mistake.