Answer
\[\underline{0.661\text{ }\Omega }\]
Work Step by Step
\[1\text{ kg}=1000\text{ g}\]
Thus, mass of copper wire is converted into grams as follows:
\[\begin{align}
& m=\left( 24.0\,\text{kg} \right)\left( \frac{1000\text{ g}}{1\,\text{kg}} \right) \\
& =24,000\text{ g}
\end{align}\]
The volume is calculated as follows:
\[V=\frac{m}{d}\]
Here, m is mass and d is density.
The density of copper is \[8.96\text{ g/c}{{m}^{3}}\]. Thus, volume is calculated as follows:
\[\begin{align}
& V=\frac{24,000\text{ g}}{8.96\text{ g/c}{{\text{m}}^{3}}} \\
& =2,679\text{ c}{{\text{m}}^{3}}
\end{align}\]
Now, \[1\text{ cm}=10\text{ mm}\].
Thus, radius of copper wire is converted into centimeters as follows:
\[\begin{align}
& r=1.63\text{ mm}\left( \frac{1\text{ cm}}{10\text{ mm}} \right) \\
& =0.163\text{ cm}
\end{align}\]
The relation between volume \[\left( V \right)\], radius \[\left( r \right)\], and length \[\left( l \right)\] is as follows:
\[\begin{align}
& \pi {{r}^{2}}\,=\,\frac{V}{l}\, \\
& \Rightarrow l=\frac{V}{\pi {{r}^{2}}} \\
\end{align}\]
Thus, length of copper wire is calculated as follows:
\[\begin{align}
& l=\frac{2,679\text{ c}{{\text{m}}^{3}}}{\left( 3.14 \right){{\left( 0.163\text{ cm} \right)}^{2}}} \\
& =32,112\text{ cm}
\end{align}\]
Now, \[1\text{ km}=1\times \text{1}{{\text{0}}^{5}}\text{ cm}\].
Thus, length of copper wire in kilometers is written as follows:
\[\begin{align}
& l=\left( 32,112\text{ cm} \right)\times \left( \frac{1\text{ km}}{{{10}^{5}}\text{ cm}} \right) \\
& =0.32112\text{ km}
\end{align}\]
The resistance of copper wire is \[2.061\text{ }\Omega \text{/km}\]. For length of \[0.32112\text{ km}\], the resistance will be as follows:
\[\begin{align}
& R=\left( 0.32112\text{ km} \right)\left( 2.061\text{ }\Omega \text{/km} \right) \\
& =0.661\text{ }\Omega
\end{align}\]
The overall resistance of the wire is \[\underline{0.661\text{ }\Omega }\].
