Question

a length of #8 copper wire (radius = 1.63 mm) has a mass of 24.0 Kg and a resistance of 2.061 Ohm per Km. What is the over all resistance of the wire?

Answer 1

V = m / ρ 
V = (23,200/8.96) × 1000 
V = 2,589,285.71 mm³ 

Now we have volume and given the radius we can solve for its length. 
L = V/πr² 
L = (2,589,285.71/(π×1.63²))/1×10^6 
L = 0.31 km 

So 
R = rL 
R = 2.061(0.31) 
R = .6389 Ω 

End.

Answer 2

Answer : The overall resistance of the wire is $6.617\times 10^{-4}ohm$

Explanation :

First we have to determine the volume of copper wire.

Density of copper wire = $0.00896kg/mm^3$

$Volume=\frac{Mass }{Density}=\frac{24kg}{0.00896kg/mm^3}=2678.57mm^3$

Now we have to determine the area.

$Area=\pi r^2$

where,

r = radius of copper wire = 1.63 mm

$Area=3.14\times (1.63mm)^2=8.343mm^2$

Now we have to determine the length of the wire.

$\text{Length of the wire}=\frac{\text{Volume of wire}}{\text{Area of wire}}$

$\text{Length of the wire}=\frac{2678.57mm^3}{8.343mm^2}=321.06mm=3.2106\times 10^{-4}km$

conversion used : $(1mm=10^{-6}km)$

Now we have to determine the overall resistance of the wire.

$\text{Overall resistance}=\text{Length of wire}\times \text{Resistance of wire}$

$\text{Overall resistance}=3.2106\times 10^{-4}km\times 2.061ohm/km$

$\text{Overall resistance}=6.617\times 10^{-4}ohm$

Therefore, the overall resistance of the wire is $6.617\times 10^{-4}ohm$