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.

Question

w=_/_

Answer 1

To find the width \( w \) of the cabinet using the volume formula \( V = lwh \), we need to rearrange the formula to isolate \( w \).

Starting with the original volume formula:

\[ V = lwh \]

To isolate \( w \), we divide both sides of the equation by \( lh \):

\[ w = \frac{V}{lh} \]

Now we can substitute the known values to find \( w \). We know:

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

Plugging these values into the formula gives:

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

Calculating the denominator:

\[ (4 , \text{ft})(5 , \text{ft}) = 20 , \text{ft}^2 \]

Now compute \( w \):

\[ w = \frac{60 , \text{ft}^3}{20 , \text{ft}^2} = 3 , \text{ft} \]

Thus, the width \( w \) of the cabinet is:

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

So, the rearranged formula is:

\[ w = \frac{V}{lh} \]