To find the volume of a rectangular prism, we use the formula:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
First, we need to convert the mixed numbers into improper fractions:
-
Length: \(4 \frac{2}{3}\)
- \(4 = \frac{12}{3}\)
- So, \(4 \frac{2}{3} = \frac{12}{3} + \frac{2}{3} = \frac{14}{3}\)
-
Height: \(3 \frac{1}{3}\)
- \(3 = \frac{9}{3}\)
- So, \(3 \frac{1}{3} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3}\)
-
Width: \(2 \frac{1}{2}\)
- \(2 = \frac{4}{2}\)
- So, \(2 \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}\)
Now, substituting these fractions into the volume formula:
\[ \text{Volume} = \left(\frac{14}{3}\right) \times \left(\frac{10}{3}\right) \times \left(\frac{5}{2}\right) \]
Calculating the product step by step:
-
First, multiply \( \frac{14}{3} \) and \( \frac{10}{3} \): \[ \frac{14 \times 10}{3 \times 3} = \frac{140}{9} \]
-
Now multiply this result by \( \frac{5}{2} \): \[ \frac{140}{9} \times \frac{5}{2} = \frac{140 \times 5}{9 \times 2} = \frac{700}{18} \]
Now, simplifying \( \frac{700}{18} \):
- Both the numerator and denominator can be divided by 2: \[ \frac{700 \div 2}{18 \div 2} = \frac{350}{9} \]
Now we convert \( \frac{350}{9} \) to a mixed number:
- Divide 350 by 9:
- \(350 \div 9 = 38\) remainder \(8\) (since \(9 \times 38 = 342\) and \(350 - 342 = 8\))
So, we can express the improper fraction as a mixed number:
\[ \frac{350}{9} = 38 \frac{8}{9} \]
Thus, the volume of the rectangular prism is
\[ \boxed{38 \frac{8}{9}} \text{ ft}^3. \]