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: