The resistance of a wire of $\displaystyle 0.01$ cm radius is $\displaystyle 7$ ohms. If the resistivity of the material of the wire is $\displaystyle 44 \times 10^{-6}$ ohm meter, calculate the length of the wire.

\[\begin{aligned} & \mathrm{r}=0.01 \mathrm{~cm}=0.01 \times 10^{-2} \mathrm{~m}, \mathrm{R}=7 \mathrm{ohm} \\ & \rho=44 \times 10^{-6} \Omega \mathrm{~m} \\ & \mathrm{~A}=\pi r^{2} \\ & R=\rho \frac{1}{\mathrm{~A}} \Rightarrow l=\frac{R \times A}{\rho} \\ & l=\frac{7 \Omega \times\left(0.01 \times 10^{-2}\right)^{2} \times \dfrac{22}{7} \mathrm{~m}^{2}}{44 \times 10^{-6} \Omega m} \\ & l=0.5 \times 10^{-2} \mathrm{~m} \end{aligned} \]