If the volume of a material is conserved under loading (Volume without force = Volume

Question

with force) what is the material’s Poisson’s ratio?
You can assume that the material is isotropic (it will behave the same in every direction).
Hint: take a cube and increase the length in one direction by a differential amount (small),
then find the differential amount that the other sides must decrease to conserve volume
(remember the material will decrease the same amount in both directions). To solve you
will have to drop any term that involves 3 differential lengths.