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 \( V = l \times w \times h \), we can rearrange the formula to isolate \( w \).

Starting with the original volume formula:

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

We want to solve for \( w \), so we can rearrange the formula as follows:

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

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

Now we can substitute the known values into this equation. The volume \( V \) is 60 ft³, the length \( l \) is 4 ft, and the height \( h \) is 5 ft.

Substituting these values in gives:

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

Calculating the denominator:

\[ 4 \text{ ft} \times 5 \text{ ft} = 20 \text{ ft}^2 \]

Now substituting back into the equation:

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

This simplifies to:

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

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