Given the formula for the volume of a box, V = lwh, which equation best represents the remaining units when justifying your rearrangement to solve for the width?

A. in.^3 = in.^3
B. in.^3/in.^2 = in.
C. in. = in.
D. in.^3/in.^2 = in.^3/in.^2

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To solve for the width \( w \) in the volume formula \( V = lwh \), you can rearrange the equation as follows:

1. Start with the original formula: \( V = lwh \)
2. Rearranging for \( w \), you get: \( w = \frac{V}{lh} \)

Now, let's examine the units involved:

- Volume \( V \) is measured in cubic inches (inΒ³).
- Length \( l \) and height \( h \) are both measured in inches (in).

When you substitute the units into the rearranged equation for width, you have:

\[
w = \frac{V}{lh} \Rightarrow w = \frac{\text{in}^3}{\text{in} \times \text{in}} = \frac{\text{in}^3}{\text{in}^2}
\]

This gives us the units for width, which turn out to be in inches (in):

\[
w = \text{in}
\]

Therefore, the equation that best represents the unit justification for the rearrangement to solve for the width is:

**B. \( \text{in}^3/\text{in}^2 = \text{in} \)**

This shows that dividing cubic inches by square inches yields inches, which is consistent with the units for width.