To find the width ($w$) of a rectangular prism using the given volume ($V$), height ($h$), and length ($l$), we can rearrange the volume formula:

$V = l \cdot w \cdot h$

Solving for $w$:

$w = \frac{V}{l \cdot h}$

Given:

• $V = 138.24$ cubic inches
• $h = 9.6$ inches
• $l = 3.2$ inches

Substitute these values into the formula:

$w = \frac{138.24}{3.2 \cdot 9.6}$

First, calculate the denominator:

$3.2 \cdot 9.6 = 30.72$

Next, divide the volume by this product:

$w = \frac{138.24}{30.72} = 4.5$

So, the width ($w$) of the rectangular prism is:

$\boxed{4.5 \text{ inches}}$

Would you like more details or have any questions?

Here are 5 questions you might want to ask:

1. How do you find the height of a rectangular prism given the volume, length, and width?
2. Can you explain the concept of surface area for a rectangular prism?
3. How would you solve for the length if the volume, width, and height are known?
4. What is the formula for the diagonal of a rectangular prism?
5. How does changing one dimension of a rectangular prism affect its volume?

Tip: When solving for a variable in a formula, isolate the variable on one side by performing the inverse operations.