The volume of a rectangular prism is given by the formula [tex]V = lwh[/tex], where [tex]l[/tex] is the length of the prism, [tex]w[/tex] is the width, and [tex]h[/tex] is the height. Which expression represents the volume of the following rectangular prism?

A. [tex]2x^2 + 13x + 18[/tex]
B. [tex]6x^3 + 27x^2 + 54x[/tex]



Answer :

Certainly! To find the volume of a rectangular prism, we use the formula for volume, [tex]\( V = l \times w \times h \)[/tex]. The volume is found by multiplying the length ([tex]\( l \)[/tex]), width ([tex]\( w \)[/tex]), and height ([tex]\( h \)[/tex]) together.

Given the expressions:
- [tex]\( l = 2x^2 + 13x + 18 \)[/tex]
- [tex]\( w \)[/tex] is not explicitly defined as a separate expression here.
- Instead, we have [tex]\( 6x^3 + 27x^2 + 54x \)[/tex], which is likely the expression for the entire volume [tex]\( V \)[/tex].

Since we are asked to identify which expression represents the volume:

1. The expression [tex]\( 2x^2 + 13x + 18 \)[/tex] is given as the length ([tex]\( l \)[/tex]).
2. The expression [tex]\( 6x^3 + 27x^2 + 54x \)[/tex] matches the form suited for the volume [tex]\( V \)[/tex].

Thus, the given volume expression for this rectangular prism is:

[tex]\[ \boxed{6x^3 + 27x^2 + 54x} \][/tex]

This represents the volume of the rectangular prism, where multiplying the length expression by suitable width and height expressions would result in this cubic polynomial.