a math problem

Post Reply New Topic

Can anyone help me understand and solve this math problem? What is an ingot?

A copper refinery produces a copper ingot weighing 150 lbs. If the copper is drawn into wire whose diameter is 8.25 mm, how many feet of copper can be obtained from the ingot? The density of copper is 8.96 g/cm^3 (that's cm is cubed).
(Assume that the wire is a cylinder whose volume is V=pi r squared h, where r is the radius and h is the height or length.)


With great appreciation...

"An ingot is a material, usually metal, that is cast into a shape suitable for further processing", according to wikipedia, so that must be 100% accurate. The question is just about converting units between metric and imperial really. I found this http://www.initium.demon.co.uk/converts/metimp.htm which works them out for you. Convert the weight to grams and then weight/density=volume (cm^3). Then find the radius (half diameter) in cm and V/(pi r^2)=h (in cm), so then you just have to convert to feet. I think that's right anyway.

Thanks MajorTom...

The problem is simple, though I can't do it now because I don't know conversion factor for converting pounds into grams. Never mind what an ingot is, it's like a small button made of the copper. Notice that the ingot and the wire would have to have the same mass and volume. Keeping that in mind, the steps are as follows:

1. First convert the mass of 150 lbs into grams (g) using the conversion factor.

2. Divide the mass in grams by the density 8.96 g/cm^3 to get the volume of the ingot in cubic centimeters (cm^3).

3. If the diameter of the wire cross section is 8.25 mm then its radius should be half that, i.e. 4.125 mm or 0.4125 cm since a millimeter is a tenth of a centimeter.

4. Now substitute the volume (in cm^3) and radius (in cm) into the equation, V = pi r squared h, and solve for h. The value for h is the length of the wire.

Thanks Jono for the excellent explanation...