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)
A. in.^3/in.^2 = in.^3/in.^2
B. in.^3 = in.^3
C. in. = in.
D. in.^3/in.^2 = in.
A. in.^3/in.^2 = in.^3/in.^2
B. in.^3 = in.^3
C. in. = in.
D. in.^3/in.^2 = in.
Answers
GPT-4o mini
To solve for the width \( w \) in the volume formula \( V = lwh \), you can rearrange the equation as follows:
1. Start with the original formula: \( V = lwh \).
2. Rearrange to solve for \( w \):
\[
w = \frac{V}{lh}
\]
When you substitute the dimensional units into this equation:
- Volume \( V \) has dimensions of cubic inches (in³).
- Length \( l \) and height \( h \) have dimensions of inches (in).
So, substituting these units gives:
\[
w = \frac{\text{in}^3}{\text{in} \cdot \text{in}} = \frac{\text{in}^3}{\text{in}^2} = \text{in}
\]
Therefore, the correct equation that represents the remaining units when justifying your rearrangement to solve for the width is:
**D. in³/in² = in.**
This option correctly shows the dimensional analysis of the rearranged equation.
1. Start with the original formula: \( V = lwh \).
2. Rearrange to solve for \( w \):
\[
w = \frac{V}{lh}
\]
When you substitute the dimensional units into this equation:
- Volume \( V \) has dimensions of cubic inches (in³).
- Length \( l \) and height \( h \) have dimensions of inches (in).
So, substituting these units gives:
\[
w = \frac{\text{in}^3}{\text{in} \cdot \text{in}} = \frac{\text{in}^3}{\text{in}^2} = \text{in}
\]
Therefore, the correct equation that represents the remaining units when justifying your rearrangement to solve for the width is:
**D. in³/in² = in.**
This option correctly shows the dimensional analysis of the rearranged equation.