Question

Enter your answer in the provided box. Copper can be drawn into thin wires. How many meters of 34-gauge wire (diameter = 6.304 × 10-3 in) can be produced from the copper in 7.00 lb of covellite, an ore of copper that is 66.0% copper by mass? (Hint: Treat the wire as a cylinder: Vof cylinder = ar'h; d of copper = 8.95 g/em³).

Answer 1

It is given that  

Mass of copper = 66 % of Mass of covellite  

= 66 × 7.00 lb / 100 = 4.62 lb

= 4.62 × 453.592 g  

= 2095.59504 g

Density of copper = 8.95 g/cm3

Recall that Volume of copper  

= Mass of copper / Density of copper  

= 2095.59504 g / 8.95 g/cm3  

= 234.145 cm3 = 234.145 × 10-6 m3

Given that Diameter of wire = 6.304 × 10-3 in

= 6.304 × 10-3 × 0.0254 m = 0.0001601216 m

Recall that Radius of wire = r = Diameter of wire / 2

= 0.0001601216 / 2 m = 0.0000800608 m  

Now , Recall that Volume of copper wire = V =   $\pi$ r2h   

where h = length of copper wire  

Therefore ,  

234.145 × 10-6 = 3.14 × (0.0000800608)2 × h

h =    11633.634 m