Solution

Poisson's ratio, $$0.4=\cfrac{\Delta d/d}{\Delta l/l}\Rightarrow\cfrac{\Delta l}{l}=\cfrac{\Delta d/d}{0.4}$$-------------(1)
$$A=\pi r^2=\cfrac{\pi d^2}{4}$$
Taking log both sides:
$$ \log A=\log {(\frac{\pi}{4})}+2\log {d}$$
Taking relative change both the sides:
$$ \cfrac{\Delta A}{A}=2\cfrac{\Delta d}{d}\\ \cfrac{\Delta d}{d}=\cfrac{1}{2}\cfrac{\Delta A}{A}=\dfrac{1}{2}\times 2\%=1\%$$------------------------------(1)
From equation (1) and (2), the percentage increase length can be given as:
$$ \cfrac{\Delta l}{l}=\cfrac{1\%}{0.4}=2.5\%$$
Option B is correct