Robert C. answered • 09/18/12

Dr. Robert can help you with Math and Science

Hi Angela.

So you are starting with an ore of copper and trying to figure out the length of pure copper wire you can make.

The strategy I will use is to convert the mass of the ore into its equivalent mass of pure copper. Then, using the density, I will figure out the volume of pure copper that we have. A wire is essentially a cylinder with a round cross section but usually with a much greater lenght. Using the formula for the volume of a cylinder and the diameter given, we will figure out how long the wire is.

5.01 lbs of ore. The since the density of the copper is given in g/ml, I will eventually have to change the mass units to be the same. I find it easiest to work in grams, rather than pounds, so lets convert into grams.

2.2 lbs = 1000 grams

This means that 1000 grams / 2.2 lbs = 1

I can always multiply an equation by 1 and not change it, though it will seem to change because the units change.

5.01 * (1000 g / 2.2 lb) = 2277.27 g

Since only 66% of this is copper, if we purify it by smelting, we would have:

2277 g * 0.66 = 1503 g of pure copper.

(Remember that when multiplying by a percentage, you move the decimal 2 places.)

Density is the mass divided by the volume.

D = m / V

Our mass, m, is 1503 g and the density given is 8.95 g / ml.

Rearranging our equation, we get V = m / Density

or

V = 1503 g / (8.95 g/ml) = 167.93 ml

The volume, V, of a cylinder is given by:

V = pi * r^2 * h, where r is radius and h is height, or in our case, h is the length of the wire. (pi is approximately 3.1415.)

We don't have the radius, but we do have the diameter. The radius is half the diameter

r = diameter/2 = 6.304 x 10^-3 in /2 = 3.152 x 10^-3 in

I can see we will have an answer in either inches or cm. When I see ml, I think cm^3. I prefer to work in cm, so I will convert that radius to cm.

2.54 cm = 1 in

3.152 x 10^-3 in * 2.54 cm/ 1 in = 8.006 x 10^-3 cm

We are almost there.

From our cylinder equation, solving for h, the length of the wire, we get

h = V / (pi* r^2)

h = (167.93 cm ^ 3) / (3.1415 * (8.006 x 10^-3 cm)^2)

(I replaced ml with cm^3.)

h = 834,000 cm or 8,340 m.

The smallest number of significant figures used was 2 (66%), so I will round my answer to 8,300 m.

Nicole C.

Robert: I liked your response, was about to type in the exact same procedure.

Angela: I hope this helped you, I think it is good advice on how to proceed through this many stepped problem

09/19/12

Jacob G.

01/20/16

Robert S.

Robert - I agree with Angela. While I didn't check any of the calculations, your step by step explanation was clear, crisp, and even humorous at one point. Nice job.

10/14/12