Ask a New Question
Menu

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

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

in.=in.
in. equals in.

in.3in.2=in.3in.2

3 answers

To find the width (w) from the formula \( V = lwh \), we can rearrange the equation:

  1. Start with \( V = lwh \).

  2. To solve for \( w \), divide both sides by \( lh \):

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

When justifying this rearrangement, we need to express the units on both sides of the equation to make sure they are consistent.

The units for volume (V) are cubic inches (in³), while the units for length (l) and height (h) are in inches (in). Therefore, when rearranging to isolate w, we can see the units clearly as follows:

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

Thus, the equation that best represents the remaining units when justifying the rearrangement to solve for the width is:

Start Fraction in. cubed over in. squared End Fraction equals in.

In=in I took the test I wish I can explain why but I guess I would need to ask my teacher to explain it in the next live lesson.

It sounds like you encountered a discrepancy in the units while rearranging the formula for the volume of a box, \( V = lwh \), to solve for one of its dimensions.

When you divide the volume (cubic inches, or in³) by the product of the length and height (which are both in inches, or in), you simplify the units as follows:

  • Volume (V): in³
  • Length (l): in
  • Height (h): in

When you divide the volume by the product of length and height, you perform this operation:

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

The result is just inches (in), which is the appropriate unit for width.

You mentioned "In=in" previously, which indicates that you might have seen that the derived units are consistent, meaning inches on both sides of an equation confirms the correctness of the calculation.

If you want to discuss it further or clarify with your teacher, you can ask specific questions about how units are derived and what each step signifies in real-world contexts. It's great that you're engaged and looking to understand!