a
\(R _{0}=1\, \Omega\)

\(\ell_{0}=1\, m\)

\(A _{0}= A\)

\(R _{1}=?\)

\(\ell_{1}=1.25\, m\)

As volume of wire remains constant so

\(A _{0} \ell_{0}= A _{1} \ell_{1} \Rightarrow A _{1}=\frac{\ell_{0} A _{0}}{\ell_{1}}\)

Now

Resistance \(( R )=\frac{\rho \ell}{ A }\)

\(\frac{ R _{0}}{ R _{1}}=\frac{\ell_{0} / A _{0}}{\rho \ell_{1} / A _{1}}\)

\(\frac{1}{ R _{1}}=\frac{\ell_{0}}{ A _{0}}\left(\frac{\ell_{0} A _{0}}{\ell_{1} \times \ell_{1}}\right) R _{1}=\frac{\ell_{1}^{2}}{\ell_{0}^{2}}=1.5625\, \Omega\)

So \% change in resistance

\(=\frac{ R _{1}- R _{0}}{ R _{0}} \times 100\, \%\)

\(=\frac{1.5625-1}{1} \times 100 \,\%\)

\(=56.25\, \%\)