The linear strain in x, y and z directions are e_x, e_y and e_z respectively. Then the volumetric strain is given by
 

• The ratio of the original length to the deformed length yields the linear strain, a word that is also defined by the transverse strain. 
• It generally happens in the parts of the body that experience longitudinal stress. The body's dimensions are currently increasing along its longitudinal axis while decreasing along its lateral axis. 
• As a result, the lateral region will shrink, which will cause the lateral areas to constrict. 
• The lateral strain in this question occurs in three different directions, hence the total lateral strain is the sum of the three strains. 
• The volumetric strain is ${\mathrm{e}}_{\mathrm{x}}+{\mathrm{e}}_{\mathrm{y}}+{\mathrm{e}}_{\mathrm{z}}$ as a result.

Hence the correct answer is ${\mathrm{e}}_{\mathrm{x}}+{\mathrm{e}}_{\mathrm{y}}+{\mathrm{e}}_{\mathrm{z}}$.