Resistivity of wire, $\mathrm{R}=\frac{\rho l}{\mathrm{A}}$

$\because$ Area $\times$ length $=$ volume

Hence, $R=\frac{\rho V}{A^{2}}$

since, $\rho \rightarrow$ constant, $V \rightarrow$ constant

$\mathrm{R} \propto \frac{1}{\mathrm{A}^{2}}$

or $\quad \mathrm{R} \propto \frac{1}{\mathrm{r}^{4}} \quad \because \quad \mathrm{A}=\pi \mathrm{r}^{2}$

$\frac{\mathrm{R}_{2}}{\mathrm{R}_{1}}=16 \Rightarrow \mathrm{R}_{2}=16 \times 100=1600 \,\Omega,$

Resistance of new wire.