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.
