Answer
(a) Decreases. (b) By a factor of $4/9$.
Work Step by Step
Resistance is equal to $$R=\frac{\rho L}{A}$$ Since the area of a circle equals $A=\pi r^2=\pi (\frac{d}{2})^2=\frac{1}{4}\pi d^2$, the formula becomes $$R=\frac{4 \rho L}{\pi d^2}$$ Since $L'=4L$ and $d'=3d$, the new resistance is equal to $$R'=\frac{4\rho (4L)}{\pi (3d)^2}=\frac{16 \rho L}{9 \pi d^2}=\frac{4}{9}R$$ This $\frac{4}{9}R$ is less than $R$; therefore, the resistance decreases.
