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. = in.
B. in.^3 over in.^2 = in.^3 over in.^2
C. in.^3 = in.^3
D. in.^3 over in.^2 = in.

1 answer

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

\[ w = \frac{V}{lh} \]

When justifying this rearrangement in terms of units, we start with the volume \( V \) which is in cubic inches \( \text{in}^3 \). The base area \( l \times h \) is in square inches \( \text{in}^2 \) (since both \( l \) and \( h \) have units of inches).

Thus, when we divide the volume by the area \( l \times h \), we have:

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

Now we need to match this to the options provided:

  • A. in. = in. (not applicable since it does not represent a ratio)
  • B. in.^3 over in.^2 = in.^3 over in.^2 (too complex and does not clearly illustrate the simplification)
  • C. in.^3 = in.^3 (not relevant for showing the units after rearrangement)
  • D. in.^3 over in.^2 = in. (this correctly captures the process of dividing cubic inches by square inches resulting in inches)

Therefore, the best answer is:

D. in.^3 over in.^2 = in.