Question

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%0D%0A60%0D%0A %0D%0Aft.%0D%0A3%0D%0A . 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%0D%0A𝑉%0D%0A=%0D%0A𝑙%0D%0A𝑤%0D%0Aℎ%0D%0A , rearrange the formula to highlight the quantity of interest. Note that volume is represented with a capital V%0D%0A𝑉%0D%0A 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

In this case, the height (\( h \)) is 5 ft, and the length (\( l \)) is 4 ft, and the volume (\( V \)) is 60 ft³.

To solve for the width (\( w \)), we can rearrange the formula as follows:

1. Start with the original volume formula:

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

2. Divide both sides by \( (l \times h) \):

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

Now, we can plug in the values we know:

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

Substituting these values in:

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

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

\[ w = 3 \, \text{ft} \]

So, the width of the cabinet is **3 ft**.