How will the resistance of the material from which the wire is made with a length of 2 m

How will the resistance of the material from which the wire is made with a length of 2 m and a cross-sectional area of 4 mm change, if it is melted and made into a cube?

L = 2 m.

S = 4 mm2 = 4 * 10-6 m2.

ρ = ρ1.

R / R1 -?

Let us express the resistance of the wire by the formula: R = ρ * L / S, where ρ is the resistivity of the material from which it is made, L is the length of the wire, S is the cross-sectional area.

Let us express the volume of the wire V according to the formula: V = L * S.

V = 2 m * 4 * 10-6 m2 = 8 * 10-6 m3.

Since the wire was melted down and a cube was made from it, the volume of the cube V will be equal to the volume of the wire V: V1 = V.

The volume of the cube V is determined by the formula: a3 = V, where a is the edge of the cube.

a = 2 * 10-2 m.

Now we express the resistance to the cube R1 by the formula: R1 = ρ1 * L1 / S1 = ρ1 * a / a2 = ρ1 / a.

R / R1 = ρ * L * a / ρ1 * S = L * a / S.

R / R1 = 2 m * 2 * 10-2 m / 4 * 10-6 m2 = 10000.

Answer: the resistance of the cube will be 10,000 less than the resistance of the wire: R / R1 = 10,000.