Claudia's family is buying a new cabinet for their home. The height of the cabinet is 5 ft, its

Question

length is 4 ft., and its volume is $60ft^{3}$ 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 \( V = lwh \), we need to rearrange the formula to solve for \( w \), the width.

Starting with the original formula:

\[ V = lwh \]

We can rearrange it for \( w \) as follows:

1. Divide both sides by the product of \( l \) and \( h \):

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

Now we can substitute in the values we have. The volume \( V \) is given as \( 60 , ft^3 \), the length \( l \) is \( 4 , ft \), and the height \( h \) is \( 5 , ft \).

So the equation becomes:

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

Calculating the denominator:

\[ 4 \cdot 5 = 20 \]

Now substituting back into the equation:

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

Thus, the width of the cabinet is:

\[ \boxed{3 , ft} \]