To find the volumetric change (ratio of change in volume to be original volume) the expression for the volume of the cylinder will be considered.
We do not to define this ratio as volumetric strain, because the volume of the material that makes cylinder is not the internal volume of the cylinder.
This volume is the volume of any substance contained in the space of the cylinder, and δV/V with mean the volumetric strain of that substance. This strain then will be related to pressure and bulk modulus of the substance.)
Thus, the volumetric strain is obtained as the sum of longitudinal strain and twice the hoop strains.
In terms of the pressure, diameter and thickness volumetric strain can be expressed as,