Calculating the volume of polynomials involves the standard equation for solving volumes, and basic algebraic arithmetic involving the first outer inner last (FOIL) method.
Things You'll Need
 Paper
 Pencil
 Calculator (optional)

Write down the basic volume formula, which is volume=lengthwidthheight.

Plug the polynomials into the volume formula.
Example: (3x+2)(x+3)(3x^22)

Utilize the first outer inner last (FOIL) method to multiply the first two equations. Further explanation of the FOIL method is found in the references section.
Example: (3x+2)*(x+3)
Becomes: (3x^2+11x+6) 
Multiply the last given equation (which you did not foil), by the new equation attained by foiling. Further explanation of basic polynomial multiplication is found in the references section.
Example: (3x^22)*(3x^2+11x+6)
Becomes: (9x^4+33x^3+18x^26x^222x12) 
Combine the like terms. The result is the volume of the polynomials.
Example: (9x^4+33x^3+18x^26x^222x12)
Becomes: Volume= (9x^4+33x^3+12x^222x12)
References
 Photo Credit calculatrice image by NoÃ© Rouxel from Fotolia.com