Question

Claudia’s family is buying a new cabinet for thei home. The height of the cabinet is 5 ft., it’s length is 4 ft., and it’s 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 the volume represented with a V in the formula.

Answer 1

To find the width of the cabinet using the volume formula \( V = l \times w \times h \), we start by rearranging the formula to highlight the width \( w \).

1. The volume formula is: \[ V = l \times w \times h \]

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

Now we can substitute the known values into the formula. We know:

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

Substituting these values into the rearranged formula for \( w \): \[ w = \frac{60}{4 \times 5} \]

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

Now, substitute back: \[ w = \frac{60}{20} = 3 , \text{ft} \]

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