e 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 *V* = *l* · *w* · *h*, where *l* is the length, *w* is the width, and *h* is the height.

Write the equation that represents the volume of the storage container in terms of its width.

To express the volume of the storage container in terms of its width, we start by using the formula for the volume of a rectangular prism:

\[
V = l \cdot w \cdot h
\]

where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.

From the problem, we know:
- The height \( h = 6 \) feet.
- The length \( l \) is 2 feet more than the width \( w \), so \( l = w + 2 \).

Substitute the given values into the volume formula:

\[
V = (w + 2) \cdot w \cdot 6
\]

Simplify the equation:

\[
V = 6(w + 2)w
\]

Distribute the terms:

\[
V = 6(w^2 + 2w)
\]

Thus, the equation for the volume in terms of the width \( w \) is:

\[
V = 6(w^2 + 2w)
\]

Would you like further clarification on any step? Here are some related questions to expand on this topic:

1. How would the volume change if the height was increased to 8 feet?
2. What would the width need to be for the volume to be 432 cubic feet?
3. How does the relationship between length and width affect the volume of the container?
4. Can you express the surface area of the storage container in terms of its width?
5. If the length was 3 feet more than the width, how would the equation for volume change?

**Tip**: When solving problems with multiple variables, it's helpful to express all variables in terms of one if possible. This simplifies the calculations!

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 V = l · w · h, where l is the length, w is the width, and h is the height. Write the equation that represents the volume of the storage container in terms of its width.

Discover how to write the volume equation of a rectangular prism where the length is 2 feet more than the width and the height is 6 feet. This problem explores key algebraic concepts, including expressing volume in terms of width and simplifying quadratic equations. Ideal for students in Grades 8-10.

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