Question

Jamie is building a box by the pool for the pool toys. They want the box’s volume to be 31.5 cubic feet. The space can hold a box that is 4.5 ft. long and 2.5 ft. wide. How high should the box be in order to meet the volume requirement? Write your answer in decimal form. (The volume of a box is length times width times height.

Answer 1

To find the height of the box, we can use the formula for the volume of a box, which is:

\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]

We know that the volume needs to be 31.5 cubic feet, the length is 4.5 feet, and the width is 2.5 feet. We can rearrange the formula to solve for the height:

\[ \text{Height} = \frac{\text{Volume}}{\text{Length} \times \text{Width}} \]

Now, substituting the known values into the equation:

\[ \text{Height} = \frac{31.5}{4.5 \times 2.5} \]

Calculating the area of the base (length times width):

\[ 4.5 \times 2.5 = 11.25 \]

Now substituting the area back into the equation for height:

\[ \text{Height} = \frac{31.5}{11.25} \]

Now doing the division:

\[ \text{Height} = 2.8 \]

Thus, the height of the box should be 2.8 feet.