Let's solve the problem step-by-step.
1. Define the variables:
- Let [tex]\( w \)[/tex] be the width of the rectangular prism.
- Let [tex]\( h \)[/tex] be the height of the rectangular prism, given as [tex]\( 6 \)[/tex] feet.
- Let [tex]\( l \)[/tex] be the length of the rectangular prism, which is given as [tex]\( 2 \)[/tex] feet more than its width, so [tex]\( l = w + 2 \)[/tex].
2. Recall the volume formula:
- The volume [tex]\( V \)[/tex] of a rectangular prism is given by the formula [tex]\( V = l \cdot w \cdot h \)[/tex].
3. Substitute the expressions for [tex]\( l \)[/tex] and [tex]\( h \)[/tex]:
- Length [tex]\( l = w + 2 \)[/tex]
- Height [tex]\( h = 6 \)[/tex] feet
This gives:
[tex]\[ V = (w + 2) \cdot w \cdot 6 \][/tex]
4. Rewrite the formula by distributing and combining like terms:
[tex]\[
V = 6w \cdot (w + 2)
\][/tex]
5. Simplify 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]
The correct answer is:
A. [tex]\(\quad V = 6w^2 + 12w\)[/tex]
