Answer:
L = 5,955 m
Explanation:
For this exercise we must use the relation
R = ρ L / A
where R is the resistance that indicates that it is 1 Ω, the resistivity is taken from the tables ρ = 2.82 10⁻⁸ Ω m, L is the length of the wire and A is the cross section.
As it indicates to us in volume of aluminum to use we divide the two terms by the length
R / L = ρ L / (A L)
the volume of a body is its area times its length, therefore
R / L = ρ L / V
R = ρ L² / V
we clear the length of the wire
L = √ R V /ρ
we reduce the volume to SI units
v = 1 cm³ (1m / 10² cm)³ = 1 10⁻⁶ m
let's calculate
L = √ (1 1 10⁻⁶ / 2.82 10⁻⁸)
L = √ (0.3546 10²)
L = 5,955 m
