Answer
28.65 m
Explanation
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
volume of wire = πr²(L)
9.6 x 10^-7 = πr²(L)
r = √(9.6 x 10^-7/π(L))
cross sectional area of wire = πr²
Formula for resistivity
R = p * length / cross SA
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
So, the wire is 28.65 m long
