R = (65 ± 1) Ω, l = (5±0.1) mm and d = (10 ± 0.5) mm. Find error in calculation of resistivity.

Given, R = 65 Ω, ∆R = I Ω,            l = 5 x 10-3 m, ∆l = 0.1 X 10-3 m,           d = 10 x 10-3 m and ∆d = 0.5 x 10-3 m∵   Resistivity, ρ=RAl or ρ=Rπ(d/2)2l=πRd24l∴                Δρρ=ΔRR+2Δdd+Δll⇒          Δρρ=165+20.5×10−310×10−3+0.1×10−35×10−3⇒           Δρρ=0.0153+0.1+0.02⇒Δρρ≈0.1353So, error in calculation of resistivity is 13.5% = 13%.