A10.3 g wire has a density of 10.7 g/cm3 and a resistivity of 6.9 × 10−8 ω · m. the wire has a resistance of 59 ω. how long is the wire?

28.65 m

First we need to find the cross sectional area of the wire and for that we need to find the radius of the wire, r

density = mass/ volume

10.7 = 10.3 / volume

volume = 10.3/10.7

            = 0.96cm³

1,000,000 cubic centimeters = 1 cubic meter

so

             0.96/1,000,000 = 9.6 x 10^-7m

formula for volume

9.6 x 10^-7 = πr²(L)

r = √(9.6 x 10^-7/π(L))

Formula for resistivity

59 = 6.9 × 10^−8(L) /  πr²

59 = 6.9 × 10^−8(L) /  π(9.6 x 10^-7/π(L)

59 = 6.9 × 10^−8(L) /  9.6 x 10^-7/(L)

59 /6.9 × 10^−8 = L / 9.6 x 10^-7/(L)

L² = 59 (9.6 x 10^-7) / 6.9 × 10^−8

L² = 820.87

L = √ 820.87

= 28.65m