Asked by Water

Claudia’s family is buying a new cabinet for their home. The height of the cabinet is 5 ft., its length is 4 ft., and its volume is 60 ft.3 . They need to know the width of the cabinet to make sure that it will fit in the space where they want to put it. Using the volume formula, V=lwh , rearrange the formula to highlight the quantity of interest. Note that volume is represented with a capital V in the formula.(1 point) w = ?/?
Answered by Water
No bot, Claudia’s family is buying a new cabinet for their home. The height of the cabinet is 5 ft., its length is 4 ft., and its volume is 60 ft.3 . They need to know the width of the cabinet to make sure that it will fit in the space where they want to put it. Using the volume formula, V=lwh , rearrange the formula to highlight the quantity of interest. Note that volume is represented with a capital V in the formula. What is the answer in fraction form?
Answered by GPT-4o mini
To find the width (w) of the cabinet using the volume formula \( V = lwh \), we can rearrange the formula to solve for width.

Starting with the equation:

\[ V = lwh \]

We can solve for \( w \) by dividing both sides of the equation by \( lh \):

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

So the rearranged formula highlighting the quantity of interest (width) is:

\[ w = \frac{V}{lh} \]
Answered by GPT-4o mini
To find the width \( w \) using the volume formula \( V = lwh \), where:

- \( V \) = volume
- \( l \) = length
- \( h \) = height

We need to rearrange the formula to solve for \( w \):

1. Start with the original formula:
\[
V = lwh
\]

2. Rearrange the formula to isolate \( w \):
\[
w = \frac{V}{lh}
\]

Given the values:
- \( V = 60 \, \text{ft}^3 \)
- \( l = 4 \, \text{ft} \)
- \( h = 5 \, \text{ft} \)

Substituting these values into the rearranged formula:
\[
w = \frac{60}{4 \cdot 5}
\]

Calculating the denominator:
\[
4 \cdot 5 = 20
\]

Now substitute back:
\[
w = \frac{60}{20}
\]

This simplifies to:
\[
w = 3
\]

So the width of the cabinet is \( 3 \, \text{ft} \).

In fraction form, the width can also be expressed as:
\[
w = \frac{3}{1}
\]