Dioptase is a mineral that contains 45.3% of copper. How many meter of wire with diameter of 0.0571 in can be produced from 3.54 lb of dioptase?

Answer 1

I believe this problem is asking for how many meters of COPPER wire with... can be produced from...

You are asked for the length of wire with a specific diameter, and you can think of this as solving for the height of a very tall cylinder (the wire).

First you need to know how much copper you will have (from the mineral) to make the wire:

45.3% of 3.54 lbs dioptase is copper, so 0.453 x 3.54 lbs = 1.60 lbs Cu

Use dimensional analysis to convert the Cu mass from lbs to g using the equivalent you would look up,

1 lb = 454 g

1.60 lbs x ^{454 g}/ _{1 lb} = 726.4 g

Use the density of Cu (look up) to convert the Cu mass to volume:

density of Cu is 8.96 g/cm³ or 8.96 g = 1 cm³ ; 726.4 g x ^{1 cm3}/ _{8.96 g} = 81.1 cm³

So the volume of the cylinder (wire) is 81.1 cm³, volume of a cylinder is V = πr²h. You are given the diameter, 0.0571 in, so you can determine the radius (¹/₂ diameter) is ^{0.0571 in}/₂ = 0.0286 in

Convert the radius from in to cm since volume is in cm³ using 1 in = 2.54 cm:

0.0286 in x ^{2.54 cm}/ _{1 in} = 0.0725 cm

Rearrange V = πr²h to solve for h: h = ^V/_πr² = ^{81.1 cm3}/ (π • (0.0725 cm)²) = 4910 cm

(divide both sides by πr²)

Convert your answer from cm to m: 4910 cm x ^{1 m}/_{100 cm} = 49.1 m Cu wire