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)

Question

Responses

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

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

in.=in.
in. equals in.

in.3=in.3

Answer 1

To solve for the width $w$ from the volume formula $V=lwh$, you can rearrange the equation as follows:

1. Start with the original formula: $V=lwh$
2. To solve for $w$, divide both sides by $lh$: $$w=\frac{V}{lh}$$

Now, let's consider the units involved:

• The volume $V$ has units of cubic inches (${\text{in}}^3$).
• The dimensions $l$ and $h$ are both measured in inches ($\text{in}$).

Thus, the units for $w$ will be derived as follows:

$$w=\frac{{\text{in}}^3}{\text{in}\cdot \text{in}}=\frac{{\text{in}}^3}{{\text{in}}^2}=\text{in}$$

This verifies that the units for width $w$ are in inches, consistent with the physical dimensions.

Now, looking at the provided options, the equation that best represents the remaining units when justifying your rearrangement to solve for the width is:

$$\text{Start Fraction in. cubed over in. squared End Fraction equals in.}$$

So, the correct response is: Start Fraction in. cubed over in. squared End Fraction equals in.