Calculate the ratio of the resistance of 20.0m of copper wire 1.8mm in diameter to 10.0m of aluminum wire 2.0mm in diameter ?

Refer to: https://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity
Resistivity of Cu, ρ(Cu) = 1.68 × 10⁻⁸ Ω m
Resistivity of Al, ρ(Al) = 2.65 × 10⁻⁸ Ω m

Resistance of Cu wire, RCu = ρ(Cu) ℓ(Cu) / A(Cu)
Resistance of Al wire, RAl = ρ(Al) ℓ(Al) / A(Al)

The ratio of the resistance of copper wire to aluminum wire, RCu/RAl
= [ρ(Cu)/ρ(Al)] ×[ℓ(Cu)/ℓ(Al)] × [A(Al)/A(Cu)]
= [ρ(Cu)/ρ(Al)] ×[ℓ(Cu)/ℓ(Al)] × [d(Al)/d(Cu)]²
= (1.68/2.65) × (20.0/10.0) × (2.0/1.8)²
= 1.56

The answer: (c) 1.56

C.    1.56

https://chemandy.com/calculators/round-wire-resistance-calculator.htm

Rcu = 17.2e-9•20/π(0.0009)²
Ral  = 15.9e-9•10/π(0.001)²

Rcu/Ral = 17.2e-9•20/π(0.0009)² / 28.2e-9•10/π(0.001)²
Rcu/Ral = 17.2•2/(0.0009)² / 128.2/(0.001)²
Rcu/Ral = (34.4/28.2 ) (0.001/0.0009)²
Rcu/Ral = (34.4/28.2 ) (10/9)²
Rcu/Ral = 1.51
(b) is closest, as values of resistivity vary with alloy, temp, etc.
(c) is possible, depends on values of resistivity from your book.






Resistance of a wire in Ω
R = ρL/A
ρ is resistivity of the material in Ω-m
L is length in meters
A is cross-sectional area in m²
A = πr², r is radius of wire in m

Volume Resistivity
resistivity Al 28.2e-9 Ω-m
resistivity Cu 17.2e-9 Ω-m or 17.2e-6 ohm-mm