To calculate the volume of the toy box, we can use the formula for the volume of a rectangular prism, which is:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
Given:
- Length = \( 3 \frac{3}{4} \) feet
- Width = \( 2 \frac{1}{2} \) feet
- Height = \( 2 \frac{1}{2} \) feet
First, let's convert the mixed numbers to improper fractions:
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Length: \[ 3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4} \]
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Width: \[ 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \]
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Height: \[ 2 \frac{1}{2} = \frac{5}{2} \text{ (same as width)} \]
Now, we will calculate the volume:
\[ \text{Volume} = \frac{15}{4} \times \frac{5}{2} \times \frac{5}{2} \]
Calculating this step by step:
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Multiply the first two fractions: \[ \frac{15}{4} \times \frac{5}{2} = \frac{15 \times 5}{4 \times 2} = \frac{75}{8} \]
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Now multiply the result by the third fraction: \[ \frac{75}{8} \times \frac{5}{2} = \frac{75 \times 5}{8 \times 2} = \frac{375}{16} \]
Now, we need to convert \(\frac{375}{16}\) into a mixed number:
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Divide 375 by 16: \[ 375 \div 16 = 23 \quad \text{(whole part)} \]
- Calculation: \(16 \times 23 = 368\)
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Find the remainder: \[ 375 - 368 = 7 \]
Thus, we can write \(\frac{375}{16}\) as: \[ 23 \frac{7}{16} \]
Therefore, the volume of the toy box is: \[ \boxed{23 \frac{7}{16}} \text{ cubic feet} \]