The resistance of a wire of $0.01\text{ cm}$ radius is $10\ \Omega$. If the resistivity of the material of the wire is $50 \times 10^{-8}\ \Omega\cdot\text{m}$, find the length of the wire.

The resistance of a uniform conductor is directly proportional to its length and inversely proportional to its cross-sectional area ($R = \rho l/A$). Here, the radius is given in centimeters, so it must first be converted to meters ($1\text{ cm} = 10^{-2}\text{ m}$) to maintain consistency with the SI unit of resistivity ($\Omega\cdot\text{m}$). The cross-sectional area of a cylindrical wire is circular, given by $A = \pi r^2$. Substituting these values into the rearranged formula $l = RA/\rho$ allows us to cancel out the $10^{-8}$ terms, simplifying the calculation to yield a length of $0.628\text{ m}$.