https://file.aiquickdraw.com/mathbot/file/172951857169170ndyz3z.jpg

To solve for \( w \), we use the formula for the volume of a cuboid:

\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]

Given:
- Volume = \( 231 \, \text{cm}^3 \)
- Length = \( 7 \, \text{cm} \)
- Height = \( 6 \, \text{cm} \)
- Width = \( w \)

The equation becomes:

\[
231 = 7 \times w \times 6
\]

Simplifying the right-hand side:

\[
231 = 42w
\]

To find \( w \), divide both sides by 42:

\[
w = \frac{231}{42} = 5.5 \, \text{cm}
\]

Thus, the value of \( w \) is \( 5.5 \, \text{cm} \).

Would you like more details or have any questions?

Here are five related questions for further practice:
1. If the height of the cuboid was doubled, what would the new volume be?
2. Calculate the surface area of the cuboid with \( w = 5.5 \, \text{cm} \).
3. If the volume was instead \( 462 \, \text{cm}^3 \), what would \( w \) be?
4. How would the volume change if the length were reduced by half?
5. What is the diagonal length of the cuboid using the dimensions \( 7 \, \text{cm} \), \( 6 \, \text{cm} \), and \( 5.5 \, \text{cm} \)?

**Tip:**

The diagram shows a cuboid with dimensions of 7 cm (length), 6 cm (height), and w cm (width). The volume of the cuboid is 231 cm^3. Calculate the value of w.

Learn how to calculate the width of a cuboid given its volume, length, and height. In this problem, we solve for the width (w) of a cuboid with dimensions 7 cm (length), 6 cm (height), and a volume of 231 cm^3. Suitable for students in Grades 6-8.

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