To find the volume of a toy box using the formula for the volume of a rectangular prism, we multiply the length, width, and height together. The formula is given by:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
Given the dimensions:
- Length = \(3 \frac{3}{4}\) feet
- Width = \(2 \frac{1}{2}\) feet
- Height = \(2 \frac{1}{2}\) feet
First, we need to convert each mixed number into an improper fraction:
-
Length:
- \(3 \frac{3}{4} = 3 + \frac{3}{4} = \frac{12}{4} + \frac{3}{4} = \frac{15}{4}\)
-
Width:
- \(2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}\)
-
Height:
- \(2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}\)
Now we can substitute these values into the volume formula:
\[ \text{Volume} = \frac{15}{4} \times \frac{5}{2} \times \frac{5}{2} \]
Calculating step by step:
-
Calculate \( \frac{5}{2} \times \frac{5}{2} = \frac{25}{4} \)
-
Next, we multiply \( \frac{15}{4} \) by \( \frac{25}{4} \):
\[ \frac{15}{4} \times \frac{25}{4} = \frac{15 \times 25}{4 \times 4} = \frac{375}{16} \]
Now we need to convert \( \frac{375}{16} \) to a mixed number:
- Divide \( 375 \) by \( 16 \):
- \( 375 \div 16 = 23\) remainder \(7\).
So, we can express \( \frac{375}{16} \) as:
\[ 23 \frac{7}{16} \]
Thus, the volume of the toy box is:
\[ \boxed{23 \frac{7}{16}} \text{ cubic feet} \]