A wire of resistance R is stretched until its length is doubled while its volume remains constant. What is the new resistance of the wire?

Resistance is given by $R = \rho \frac{l}{A}$. When the wire is stretched to double its length ($l' = 2l$) with volume remaining constant, its cross-sectional area decreases to half ($A' = A / 2$). The new resistance is $R' = \rho \frac{2l}{A/2} = 4 \left(\rho \frac{l}{A}\right) = 4R$.