The radius (r) , length (l) and resistance (R) of a metal wire was...

The resistance of the wire is given as, $R = \dfrac{ρl}{A}$

Therefore, $ρ = R\dfrac{A}{l}$

$ρ = R\dfrac{\left(\pi{r}^{2}\right)}{l}$

For percentage error, we can write $\dfrac{\Deltaρ}{ρ} = \dfrac{\DeltaR}{R} + 2\dfrac{\Deltar}{r} + \dfrac{\Deltal}{l}$

$\dfrac{\Deltaρ}{ρ} \times 100 = \dfrac{\DeltaR}{R} \times 100 + 2\dfrac{\Deltar}{r} \times 100 + \dfrac{\Deltal}{l} \times 100$

$= \left(\dfrac{10}{100} + 2 \times \dfrac{0 .05}{0 .35} + \dfrac{0 .2}{15}\right) \times 100$

$= \left(\dfrac{1}{10} + \dfrac{2}{7} + \dfrac{1}{75}\right) \times 100$

Hence, $\dfrac{\Deltaρ}{ρ} = 39 .9$