Respuesta :
Covellite ore contains 66% copper by mass thus, in 5.01 lb of covellit, mass of copper will be :
[tex]m_{Cu}=\frac{66}{100}\times 5.01 lb=3.3066 lb[/tex]
Converting mass into grams,
1 lb=453.592 g
Thus, 5.01 lb=2272.498 g
The density of copper is [tex]8.95 g/cm^{3}[/tex], calculate volume as follows:
[tex]V=\frac{m}{d}=\frac{2272.498 g}{8.95 g/cm^{3}}=253.91 cm^{3}[/tex]
Comparing this volume of cylinder because shape of wire is cylindrical.
[tex]V=\pi r^{2}h=253.91 cm^{3}[/tex]
Since, 34 gauge=0.00630 inch
Convert inch into cm,
1 inch=2.54 cm
Thus,
0.00630 inch=0.016002 cm
The diameter of wire is 0.016002 cm, calculate radius as follows:
[tex]Radius =\frac{diameter}{2}=\frac{0.016002}{2}=0.008 cm[/tex]
Rearranging equation for volume and putting the values,
[tex]h=\frac{253.91 cm^{3}}{(3.14)(0.008cm)^{2}}=1.26\times 10^{6}cm[/tex]
1 cm=0.01 m thus,
[tex]1.26\times 10^{6}cm=1.26\times 10^{6}\times 0.01 m=1.26\times 10^{4}m[/tex]
Thus, the length of wire is [tex]1.26\times 10^{4}m[/tex].
