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

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Discussion Overview

The discussion revolves around converting the volume of a 16-gauge copper wire into its length, specifically addressing the calculations needed to transition from volume to linear measurements. The context includes homework-related queries and mathematical reasoning involving geometry and unit conversions.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant outlines the problem of determining the length of wire in a 1.00-lb spool of 16-gauge copper wire, noting the diameter and density of copper.
  • Another participant asks how to convert cubic centimeters to cubic meters and inquires about the number of inches in a meter.
  • A participant corrects a misunderstanding regarding the conversion factor, clarifying that 100 cm, not inches, equals 1 meter.
  • One participant explains that cubic conversions require applying the conversion factor three times due to the nature of volume.
  • A participant suggests that understanding the relationship between the diameter of the wire and its length is crucial for solving the problem.
  • Another participant advises calculating the cross-sectional area of the wire and relates the volume of the wire to its length through the formula for the volume of a cylinder.
  • A participant shares their calculation of the volume of wire but expresses confusion over the resulting length being too large.
  • One participant reminds another to ensure they are using the radius in their calculations and to check their units.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding unit conversions and the relationships between volume, diameter, and length. There is no consensus on the correct approach to the problem, and multiple viewpoints on the necessary calculations are presented.

Contextual Notes

Participants have not fully resolved the mathematical steps required to convert volume to length, and there are unresolved assumptions regarding unit conversions and the application of formulas.

kevinnn
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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!
 
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How would you go from cubic centimeters to cubic meters? How many inches are in 1 meter?
 
100 inches in one meter. I can't take the cube root of both though so that's where I get stuck.
 
kevinnn said:
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
 
Cubic, just means the conversion occurs as a factor three times, so the conversion ratio for the unit must also be done three times.
 
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.
 
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?
 
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.
 
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.
 
  • #10
Make sure you're using the radius and have the correct units.
 
  • #11
ohh thank you. That was a dumb mistake.
 

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