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.

Answer 1

To find the width (w) of the cabinet using the volume formula \( V = l \times w \times h \), we need to rearrange the formula to solve for width \( w \).

Start with the volume formula: \[ V = l \times w \times h \]

To isolate \( w \), divide both sides of the equation by \( l \) and \( h \): \[ w = \frac{V}{l \times h} \]

Now we have the rearranged formula highlighting the quantity of interest (width): \[ w = \frac{V}{l \times h} \]

Given the height (\( h = 5 \) ft), length (\( l = 4 \) ft), and volume (\( V = 60 \) ft³), you can now substitute these values into the equation to find the width: \[ w = \frac{60 , \text{ft}^3}{4 , \text{ft} \times 5 , \text{ft}} = \frac{60 , \text{ft}^3}{20 , \text{ft}^2} \] \[ w = 3 , \text{ft} \]

Therefore, the width of the cabinet is 3 ft.