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 = Box/Box

Answer 1

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

The volume \( V \) can be expressed in terms of length (\( l \)), width (\( w \)), and height (\( h \)): \[ V = lwh \]

We want to isolate \( w \). To do this, we can divide both sides of the equation by \( lh \): \[ w = \frac{V}{lh} \]

Now, let's substitute the known values into the equation. We have:

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

Now plug in these values: \[ w = \frac{60}{4 \times 5} \]

Calculating the denominator: \[ 4 \times 5 = 20 \]

Now, substituting this value into the equation for width: \[ w = \frac{60}{20} = 3 , \text{ft} \]

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