Question

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?(1 point)
Responses

in.=in.
in. equals in.

in.3in.2=in.
Start Fraction in. cubed over in. squared End Fraction equals in.

in.3=in.3
in. cubed equals in. cubed

in.3in.2=in.3in.2
Start Fraction in. cubed over in. squared End Fraction equals Start Fraction in. cubed over in. squared End Fraction

Answer 1

To rearrange the formula for the volume of a box \( V = lwh \) to solve for the width \( w \), you would divide both sides by \( lh \). The original equation can be expressed as:

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

Now, when justifying this rearrangement in terms of units, you're essentially wanting to confirm that the units are consistent throughout the equation. The volume \( V \) is measured in cubic inches (in³), and the product of the length \( l \) and height \( h \) is measured in square inches (in²).

Thus, when you divide cubic inches by square inches, you get:

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

This means the units of width \( w \) will indeed just be in inches (in), which makes sense.

Among the provided responses, the equation that best represents the remaining units and justifies the rearrangement to solve for width is:

**in.³/in.² = in.**

This indicates that when you divide cubic inches by square inches, you are left with inches, which confirms the correctness of the rearrangement.