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.

Answer 1

To find the width of the cabinet using the volume formula, we start with the formula for volume:

\[ V = l \times w \times h \]

Where:

• \( V \) is the volume,
• \( l \) is the length,
• \( w \) is the width,
• \( h \) is the height.

We want to solve for the width \( w \). To do this, we can rearrange the formula as follows:

1. Divide both sides by \( h \): \[ \frac{V}{h} = l \times w \]

2. Next, divide both sides by \( l \): \[ w = \frac{V}{l \times h} \]

Now, we have \( w \) isolated:

\[ w = \frac{V}{l \times h} \]

Now we can substitute the given values into the equation. We know:

• \( V = 60 , \text{ft}^3 \)
• \( l = 4 , \text{ft} \)
• \( h = 5 , \text{ft} \)

Substituting these values:

\[ w = \frac{60}{4 \times 5} \]

Calculating the denominator:

\[ 4 \times 5 = 20 \]

Now substituting that back into the equation:

\[ w = \frac{60}{20} = 3 \]

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