To find the volume \( V \) of a rectangular prism, you use the formula:
\[ V = B \times H \]
where \( B \) is the area of the base and \( H \) is the height. The base \( B \) can be calculated using the length and width.
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Determine the base area \( B \): \[ \text{Width} = 3 \frac{1}{4} = \frac{13}{4} , \text{inches} \] \[ \text{Length} = 5 \frac{1}{8} = \frac{41}{8} , \text{inches} \]
Now, calculate the area of the base: \[ B = \text{Width} \times \text{Length} = \left(\frac{13}{4}\right) \times \left(\frac{41}{8}\right) \] \[ B = \frac{13 \times 41}{4 \times 8} = \frac{533}{32} , \text{square inches} \]
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Now, convert the height to an improper fraction: \[ \text{Height} = 7 \frac{3}{8} = \frac{59}{8} , \text{inches} \]
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Calculate the volume \( V \): \[ V = B \times H = \left(\frac{533}{32}\right) \times \left(\frac{59}{8}\right) \] \[ V = \frac{533 \times 59}{32 \times 8} = \frac{31447}{256} , \text{cubic inches} \]
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Convert \(\frac{31447}{256}\) to a mixed number:
- Divide 31447 by 256: \[ 31447 \div 256 \approx 122.75 \quad \text{(where } 122 \text{ is the whole number)} \]
- To find the remainder: \[ 256 \times 122 = 31232 \] \[ 31447 - 31232 = 215 \]
Therefore, the volume as a mixed number is: \[ V = 122 \frac{215}{256} \]
Thus, the volume of the rectangular prism is: \[ \boxed{122 \frac{215}{256}} , \text{cubic inches} \]