12. The volume of a rectangular prism can be found using the formula V = lwh. The length is equal to (x + 2)in, the width is equal to (2x - 5) in, and the height is equal to (x + 4) in. What is the value of the cubic volume of the rectangular prism?
A. V = (2x^3 + 7x^2 - 14x - 40)in^3
B. V = (2x^3 - 5x^2 - 12x + 40)in^3
C. V = (4x + 1)in^3
D. V = (2x^2 - 4x + 1)in^3
To find the cubic volume of the rectangular prism, we substitute the given expressions for length, width, and height into the formula V = lwh.
V = (x + 2)(2x - 5)(x + 4)
V = (2x^2 + 4x - 5x - 10)(x + 4)
V = (2x^2 - x - 10)(x + 4)
V = 2x^3 + 8x^2 - x^2 - 4x - 40
V = 2x^3 + 7x^2 - 4x - 40
Therefore, the cubic volume of the rectangular prism is V = (2x^3 + 7x^2 - 4x - 40)in^3, which corresponds to option:
A. V = (2x^3 + 7x^2 - 14x - 40)in^3.