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?
in. = in.
in. cubed/in. squared = in.
in. cubed/in. squared = in. cubed/in. squared
in. cubed = in. cubed
in. = in.
in. cubed/in. squared = in.
in. cubed/in. squared = in. cubed/in. squared
in. cubed = in. cubed
Answers
Answered by
GPT-4o mini
To rearrange the formula for the volume of a box, \( V = lwh \), to solve for the width \( w \), you can isolate \( w \) by dividing both sides by \( lh \):
\[
w = \frac{V}{lh}.
\]
Now, let's analyze the units:
- Volume \( V \) is measured in cubic inches (in³).
- Length \( l \) and height \( h \) are both measured in inches (in).
So, when we substitute the units into the equation for \( w \), we have:
\[
w = \frac{V}{lh} \rightarrow w = \frac{\text{in}^3}{\text{in} \times \text{in}} = \frac{\text{in}^3}{\text{in}^2} = \text{in}.
\]
Thus, when justifying the rearrangement with units, the equation that BEST represents the remaining units is:
**in. cubed/in. squared = in.**
This shows how the cubic inches (volume) divided by square inches (area) results in linear inches, which is the unit for width \( w \).
\[
w = \frac{V}{lh}.
\]
Now, let's analyze the units:
- Volume \( V \) is measured in cubic inches (in³).
- Length \( l \) and height \( h \) are both measured in inches (in).
So, when we substitute the units into the equation for \( w \), we have:
\[
w = \frac{V}{lh} \rightarrow w = \frac{\text{in}^3}{\text{in} \times \text{in}} = \frac{\text{in}^3}{\text{in}^2} = \text{in}.
\]
Thus, when justifying the rearrangement with units, the equation that BEST represents the remaining units is:
**in. cubed/in. squared = in.**
This shows how the cubic inches (volume) divided by square inches (area) results in linear inches, which is the unit for width \( w \).
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