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.(1 point)

Question

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.(1 point)

Answer 1

To rearrange the formula to highlight the quantity of interest, we can divide both sides of the equation by the length and height of the cabinet:

V = lwh

Dividing both sides by lh:

V/(lh) = (lwh)/(lh)

Simplifying:

V/(lh) = w

Therefore, the formula for the width (w) of the cabinet in terms of volume (V), length (l), and height (h) is:

w = V/(lh)

Answer 2

To rearrange the volume formula to highlight the quantity of interest (width in this case), follow these steps:

1. Start with the volume formula: V = lwh.
2. Divide both sides of the equation by "lh". This will isolate the width (w) on one side of the equation: V / (lh) = w.
3. The quantity of interest, which is the width, is now highlighted on the right side of the equation. So the rearranged formula is: w = V / (lh).

Therefore, the rearranged formula to find the width of the cabinet is: w = V / (lh).

Answer 3

To find the width of the cabinet, we need to rearrange the volume formula to solve for the width. The volume formula is given as V = lwh, where V represents the volume, l represents the length, w represents the width, and h represents the height.

To highlight the quantity of interest, which is the width (w), we need to isolate it on one side of the equation. Let's rearrange the formula step by step:

Step 1: Start with the original formula: V = lwh

Step 2: Divide both sides of the equation by lh to isolate w: V/(lh) = (lwh)/(lh)

Step 3: Simplify the right side of the equation by canceling out the terms: V/(lh) = w

So, the rearranged formula to find the width of the cabinet is w = V/(lh).

Now, we can substitute the given values into the formula to calculate the width. Given that the volume (V) is 60 ft³, the length (l) is 4 ft, and the height (h) is 5 ft, we can plug in these values:

w = 60 ft³ / ((4 ft) * (5 ft))

Finally, solve the equation:

w = 60 ft³ / (20 ft²)

w = 3 ft

Therefore, the width of the cabinet is 3 ft.