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?

Question

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

Answer 1

To rearrange the formula for the volume of a box, \( V = lwh \), to solve for the width \( w \), you would start by isolating \( w \):

1. Rearranging the equation gives \( w = \frac{V}{lh} \).

Now let's analyze the units in the equation:

• The volume \( V \) is in cubic inches (in³).
• The length \( l \) and height \( h \) are both in inches (in).

So, when you express \( w \):

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

From this analysis, the equation that best represents the remaining units when justifying the rearrangement to solve for the width is:

D) in³ / in² = in.