A student measures the resistance, diameter, and length of a wire...

The resistivity of a wire is given by the formula:

$\rho = \dfrac{R A}{l} = \dfrac{R \pi d^2}{4 l}$

The maximum percentage error in resistivity is given by the sum of the percentage errors of the individual quantities, taking into account their powers:

$\dfrac{\Delta \rho}{\rho} \times 100 = \left( \dfrac{\Delta R}{R} + 2\dfrac{\Delta d}{d} + \dfrac{\Delta l}{l} \right) \times 100$

Calculating the individual percentage errors:
Percentage error in $R = \dfrac{0.5}{25.0} \times 100 = 2\%$
Percentage error in $d = \dfrac{0.02}{1.00} \times 100 = 2\%$
Percentage error in $l = \dfrac{0.5}{100.0} \times 100 = 0.5\%$

Substituting these values into the error equation:

$\dfrac{\Delta \rho}{\rho} \times 100 = 2\% + 2(2\%) + 0.5\%$

$\dfrac{\Delta \rho}{\rho} \times 100 = 2\% + 4\% + 0.5\% = 6.5\%$

Answer: $6.5\%$