Question

When a thin metal wire is stretched load a load the fractonal change in its volume is proportional to?

Answer 1

Poisson's ration for most metals is close to 1/3. That means for a stretch of 1%, you get a reduction in the diameter of 0.33% Adding up the changes in all three dimensions gives you a volume increase of 0.33%. (The "rubber-band" deformation with no volume change corresponds to a Poisson's Ration of 1/2.)