Well there are many methods to the calculate volume, but I will answer in context of modern structural design softwares.
Modern structural design software calculates the volume of every section so as to determine the minimum and the maximum percentage of reinforcement in accordance with different codal provisions.
Now, a section may be a beam, column, slab etc. We can also design sections with arbitrary geometry such as trapezoidal sections, curved sections, tapered section etc.
Calculation of this much amount of random sections is a cumbersome task. So, defining a formula for each section is not a wise decision.
That is why softwares like ETABS, staad.pro uses numerical methods. Basically volume may be calculated for any random shape using triple integral. click here- Volume – Wikipedia
Now, since in structural analysis, we use shape function with predefined trial functions (refer to any FEA book), we can explicitly calculate the volume of every element of a section using Gauss quadrature, newton cotes method etc.
Please refer to any FEA book or course so as to understand the concept of elements.
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