Question

If the copper is drawn into wire whose diameter is 9.50 mm, how many feet of copper can be obtained from the ingot? The density of copper is 8.94 g/cm3. (Assume that the wire is a cylinder whose volume is V=πr2h, where r is its radius and h is its height or length.)

Answer 1

Answer:

The length of the wire = 352.66 feet.

Explanation:

A copper refinery produces a copper ingot weighing 150 lb. If the copper is drawn into wire whose diameter is 9.50 mm, how many feet of copper can be obtained from the ingot? The density of copper is 8.94 g/cm3. (Assume that the wire is a cylinder whose volume is V = πr2h, where r is the radius and h is its height or length.)

Step 1: Convert lb to kg

150 lb = 68.0389 kg

Step 2: Calculate volume of copper

Volume = mass / density

Volume = 68038.9 grams / 8.94 g/cm³

Volume = 7610.6 cm³ Cu

Step 3: Calculate length of wire

The diameter of the wire is 9.50 mm, so the radius is half of that (4.75 mm), or 0.475 cm.

The total "volume" of the wire is πr²h = (π)*(0.475 cm)²(h) = 0.708h = 7610 cm^3

7610 = 0.708h

h = 10749 cm = length of wire

The length of the wire = 352.66 feet.