The storage container below is in the shape of a rectangular prism with a height of 6 feet and a length that is 2 feet more than its width.
Recall that the formula for the volume of a rectangular prism is [tex]V = l \cdot w \cdot h[/tex], where [tex]l[/tex] is the length, [tex]w[/tex] is the width, and [tex]h[/tex] is the height. Write the equation that represents the volume of the storage container in terms of its width.
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]
