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

Question

. 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, you 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.

To isolate the width (\( w \)), you can rearrange the formula as follows:

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

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

Now, the formula for width (\( w \)) is highlighted:

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

With Claudia’s cabinet dimensions:

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

We can substitute these values into the rearranged formula to find the width:

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

Calculating this gives:

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

Therefore, the width of the cabinet is 3 feet.