Copper can be drawn into thin wires. How many meters of 34-gauge wire (diameter = 6.304 × 10ିଷ 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: V = πrଶh and d = 8.95 g cmଷ ⁄ )

Therefore, the length of copper wire in meters = 8321.01 m

Explanation:

Mass of covellite = 5.01 lb

Note: 1 lb = 453.592 g, therefore mass of covellite in grams = 5.01 * 453.592 = 2272.496 g

Mass copper in the covellite = 66% * 2272.496 = 1499.847 g of copper

Volume of copper in 1499.847 g of copper is obtained using the formula; volume = mass/ density

volume of copper = 1499.847 g/ 8.95 gcm⁻³ = 167.58 cm³

since the wire is considered to be a cylinder, the length of the wire is same as the height of a cylinder

Using the formula, V = πr²h

h = V/πr²

radius of wire, r = diameter/2

diameter = 6.304 * 10⁻³ in.

1 inch = 2.54 cm, therefore radius of wire = (6.304 * 10⁻³ in * 2.54 cm)/(2 * 1 in) = 8.00608 * 10⁻³ cm

h = 167.58 cm³/ {3.142 * (8.00608 * 10⁻³ cm)²}

h = 832101.211 cm

1 cm = 0.01 m

Therefore, the length of copper wire in meters = 832101.211 * 0.01 m = 8321.01 m

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