Question

a wire of certain radius is stretched so that it's radius decrease by a factor n. calculate its new resistance

Answer 1

R=rho*l/A

R=resistance of wire
rhob= resistivity of material
l = length of wire
A = cross sectional area of wire

A=pi*r^2

if r decrease by a factor n

then new r is r/n

then substitute the new radius in the above fromulae and find the new resistance

Answer 2

The volume of the wire should remain constant. 
V = pi r^2 L 
If the radius decreases by a factor of n, the length must increase by a factor of n^2 to keep the volume constant. 
V = pi (r/n)^2 (n^2 L) 
The formula for resistance is 
R = p L/A = p L/(pi r^2) 
Increase L by n^2 and decrease r by n: 
R_new = p (n^2 L)/(pi (r/n)^2) = n^4 p L/A = n^4 R 
Its new resistance is n^4 times the old.