To find the volume of the toy box, we can use the formula for the volume of a rectangular prism:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
Given measurements:
- Length = \(3 \frac{3}{4}\) feet
- Width = \(2 \frac{1}{2}\) feet
- Height = \(2 \frac{1}{2}\) feet
First, we convert these mixed numbers to improper fractions.
-
Convert \(3 \frac{3}{4}\): \[ 3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4} \]
-
Convert \(2 \frac{1}{2}\): \[ 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \]
-
Convert \(2 \frac{1}{2}\) again (same as above): \[ 2 \frac{1}{2} = \frac{5}{2} \]
Now we can calculate the volume:
\[ \text{Volume} = \frac{15}{4} \times \frac{5}{2} \times \frac{5}{2} \]
First, calculate the product of the fractions: \[ \text{Volume} = \frac{15 \times 5 \times 5}{4 \times 2 \times 2} = \frac{375}{16} \]
Next, we convert \(\frac{375}{16}\) to a mixed number:
- Divide 375 by 16:
- 16 goes into 375, 23 times, since \(16 \times 23 = 368\).
- The remainder is \(375 - 368 = 7\).
Thus, we can write: \[ \frac{375}{16} = 23 \frac{7}{16} \]
Therefore, the volume of the toy box is:
\[ \boxed{23 \frac{7}{16}} \text{ cubic feet} \]