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 \( V = l \times w \times h \), we will rearrange the formula to solve for the width \( w \).

Given:

• Volume \( V = 60 \) ft³
• Length \( l = 4 \) ft
• Height \( h = 5 \) ft

We can rearrange the formula as follows:

1. Start with the original volume formula: \[ V = l \times w \times h \]

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

Now, substitute the known values into this rearranged formula:

\[ w = \frac{60 \text{ ft}^3}{4 \text{ ft} \times 5 \text{ ft}} \]

Now calculate:

1. Calculate \( l \times h \): \[ 4 \text{ ft} \times 5 \text{ ft} = 20 \text{ ft}^2 \]

2. Now substitute this back into the equation for \( w \): \[ w = \frac{60 \text{ ft}^3}{20 \text{ ft}^2} = 3 \text{ ft} \]

Thus, the width of the cabinet is \( 3 \) ft.