To solve the problem, let's break it down step-by-step.
1. Identify the dimensions of the rectangular prism:
- The height [tex]\( h \)[/tex] is given as 6 feet.
- The width [tex]\( w \)[/tex] remains as [tex]\( w \)[/tex].
- The length [tex]\( l \)[/tex] is 2 feet more than the width, hence [tex]\( l = w + 2 \)[/tex].
2. Write the formula for the volume of a rectangular prism:
[tex]\[
V = l \cdot w \cdot h
\][/tex]
Substituting the given dimensions for length, width, and height, we get:
[tex]\[
V = (w + 2) \cdot w \cdot 6
\][/tex]
3. Simplify the expression:
[tex]\[
V = 6 \cdot w \cdot (w + 2)
\][/tex]
[tex]\[
V = 6w \cdot (w + 2)
\][/tex]
4. Expand the expression:
[tex]\[
V = 6w \cdot w + 6w \cdot 2
\][/tex]
[tex]\[
V = 6w^2 + 12w
\][/tex]
Therefore, the equation that represents the volume of the storage container in terms of its width [tex]\( w \)[/tex] is:
[tex]\[
V = 6w^2 + 12w
\][/tex]
So, the correct answer is:
[tex]\[
\text{B.} \quad V = 6w^2 + 12w
\][/tex]
