The resistance of a wire is given by
where
is the resistivity of the material, L the length of the wire and A its cross-sectional area.
In the problem,
and L remain the same, while A changes because the radius changes. The area is given by:
This means that if we double the radius (2r), the area becomes
And therefore, the new value of the resistance is
So, when the radius is doubled, the resistance becomes
of its original value.
where
In the problem,
This means that if we double the radius (2r), the area becomes
And therefore, the new value of the resistance is
So, when the radius is doubled, the resistance becomes