How Many Meters of 34-Gauge Wire Can Be Made from 5.01 lb of Covellite?

[metalmagik]

Homework Statement

Copper can be drawn into thin wires. How many meters of 34-gauge wire (diameter = 6.304 x 10^-3 in) can be produced from the copper in 5.01 lb of covellite, an ore of copper that is 66% copper by mass? (Hint: Treat the wire as a cylinder. d of copper = 8.95 g/cm^3)

Homework Equations

V = (pi)(r^2)(h)

The Attempt at a Solution

So I used the formula for Volume of a cylinder, V = (pi)(r^2)(h) and plugged in half of the given diameter for r and then the whole diameter for h. And I got 1.968 x 10^-7 cubic inches. How should I go about doing the rest of the problem? It's really confusing me. Help please!

 

[edziura]

Think of it this way. You are given a certain mass of covellite (5.01 lb = 2273 grams), of which 66% is copper (1500 grams). You know the density of copper, so you can calculate the volume of copper available, since

d = $$\frac{m}{V}$$

Once you calculate the volume, you want to form the copper into the shape of a cylinder (wire), and the volume of the cylinder = volume of copper available. For a cylinder, the volume can be written

V = pi $$r^{2}$$ L

where L is the length we wish to find. Take V from the first part and solve this equation for L.

 

[metalmagik]

Ah man I totally get it now. I wasn't thinking of the variable in the Volume formula as length, my book labels it as h, which I interpreted for height.

Thanks so much edziura! That really helped me to clarify my thinking, all this stuff with mass is so difficult, its all over my homework which is due tomorrow, and my professor hasn't even gotten past dimensional analysis in lecture! Thanks again.

 

[edziura]

Your welcome.