The radius ($r$), length ($l$) and resistance ($R$) of a metal wire was measured in the laboratory as\n$r = (0.35 \pm 0.05)\ \text{cm}$\n$R = (100 \pm 10)\ \Omega$\n$l = (15 \pm 0.2)\ \text{cm}$\nThe percentage error in the resistivity of the material of the wire is: A). $25.6\%$ B). $39.9\%$ C). $37.3\%$ D). $35.6\%$

The correct answer is $39.9\%$. Resistivity: $\rho = \frac{R \cdot A}{l} = \frac{R \cdot \pi r^2}{l}$\nRelative error:\n$\frac{\Delta\rho}{\rho} = \frac{\Delta R}{R} + 2\frac{\Delta r}{r} + \frac{\Delta l}{l}$\n$= \frac{10}{100} + 2 \times \frac{0.05}{0.35} + \frac{0.2}{15}$\n$= 10\% + 2 \times 14.28\% + 1.33\%$\n$= 10\% + 28.57\% + 1.33\%$\n$\approx 39.9\%$

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The radius ( $r$ ), length ( $l$ ) and resistance ( $R$ ) of a metal wire was measured in the laboratory as $r = (0.35 \pm 0.05)\ \text{cm}$ $R = (100 \pm 10)\ \Omega$ $l = (15 \pm 0.2)\ \text{cm}$ The percentage error in the resistivity of the material of the wire is:

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