Question

In cubic feet, what’s is the volume of a toy box measuring 3 3/4 feet long, 2 1/2 feet wide, and 2 1/2 feet tall? Use the volume formula to solve, write your answer as a mixed number

Answer 1

To find the volume of the toy box, we use the volume formula for a rectangular prism:

\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]

In this case, we have:
- Length = \(3 \frac{3}{4}\) feet
- Width = \(2 \frac{1}{2}\) feet
- Height = \(2 \frac{1}{2}\) feet

First, we need to convert these mixed numbers into improper fractions.

1. Convert \(3 \frac{3}{4}\):
\[
3 \frac{3}{4} = 3 + \frac{3}{4} = \frac{12}{4} + \frac{3}{4} = \frac{15}{4}
\]

2. Convert \(2 \frac{1}{2}\):
\[
2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}
\]

So, the dimensions are:
- Length = \(\frac{15}{4}\) feet
- Width = \(\frac{5}{2}\) feet
- Height = \(\frac{5}{2}\) feet

Now, we can substitute these values into the volume formula:

\[
\text{Volume} = \left(\frac{15}{4}\right) \times \left(\frac{5}{2}\right) \times \left(\frac{5}{2}\right)
\]

Calculate step by step:

1. First, multiply the width and height:
\[
\left(\frac{5}{2}\right) \times \left(\frac{5}{2}\right) = \frac{25}{4}
\]

2. Now we have:
\[
\text{Volume} = \frac{15}{4} \times \frac{25}{4}
\]

3. Multiply the numerators and the denominators:
\[
\frac{15 \times 25}{4 \times 4} = \frac{375}{16}
\]

Next, we can convert \(\frac{375}{16}\) into a mixed number.

1. Divide 375 by 16:
- \(375 \div 16 = 23\) (whole number)
- Remainder: \(375 - (16 \times 23) = 375 - 368 = 7\)

So, we can write this as:
\[
\frac{375}{16} = 23 \frac{7}{16}
\]

Thus, the volume of the toy box is

\[
\boxed{23 \frac{7}{16}} \text{ cubic feet.}
\]