Question

Copper can be drawn into thin wires. How many meters of 34-gauge wire (diameter = 6.304 x 10^-3 in.) can be produced from the copper in 6.95 lb of covellite, an ore of copper is 66.0% copper by mass? (Hint: Treat the wire as a cylinder: V for cylinder = (pi)(r^2)(h); d of copper = 8.95 g/cm^3)

Answer 1

Answer:

11,547.67 meters of copper can be drawn.

Explanation:

Mass of mineral = 6.95 lb = 6.95 × 453.592 = 3,152.46 g

1 lbs = 453.592 g

An ore of copper is 66.0% copper by mass, So mas of copper in  3,152.46 grams of ore= m

$m = \frac{66.0}{100}\times 3,152.46 g=2080.63 g$

Volume of copper = V

Density of copper = d = $8.95 /cm^3$

$V=\frac{m}{d}=\frac{2080.63 g}{8.95 /cm^3}=232.47 cm^3$

Diameter of the wire drawn from the $232.47 cm^3$ of copper= d

d = $6.304\times 10^{-3} inch=6.304\times 10^{-3}\times 2.54 cm=0.01601 cm$

(1 inch= 2.54 cm)

Radius of the wire= r = 0.5 ×  d =0.5 × 0.01601 =0.008005 cm

Length of the wire = h

Volume of the cylindrical wire = $\pi r^2 h$

$V=\pi r^2 h$

$232.47 cm^3=3.14\times (0.008005 cm)^2\times h$

Solving for h :

h =1,154,767.015 cm

1 cm = 0.01 m

h = 1,154,767.015 cm = 1,154,767.015× 0.01 m = 11,547.67 m

11,547.67 meters of copper can be drawn.