The length of a certain wire is kept same while its radius is doubled. what is the new resistivity of this wire?

The text does not specify whether the resistance R of the wire must be kept the same or not: here I assume R must be kept the same.

The relationship between the resistance and the resistivity of a wire is

where
is the resistivity
A is the cross-sectional area
R is the resistance
L is the wire length

the cross-sectional area is given by

where r is the radius of the wire. Substituting in the previous equation ,we find


For the new wire, the length L is kept the same (L'=L) while the radius is doubled (r'=2r), so the new resistivity is

Therefore, the new resistivity must be 4 times the original one.

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