Gauge is a term used to describe the size of a wire: The greater the gauge, the smaller the wire diameter. At room temperature, 6-gauge wire has a diameter of \(4.115 \mathrm{~mm}\), and 22-gauge wire has a diameter of \(0.644 \mathrm{~mm}\). For copper, how long would a wire of each gauge need to be to have a resistance of \(0.5 \Omega\left[\sigma_{\text {copper }}=\right.\) \(\left.5.9 \times 10^{7} \mathrm{~A} /(\mathrm{V} \cdot \mathrm{m})\right]\) ?