To find the volume \( V \) of a rectangular prism, we use the formula:
\[ V = B \times h \]
where \( B \) is the area of the base (length \( l \) times width \( w \)) and \( h \) is the height.
Given:
- Height \( h = 3 \frac{2}{5} \) ft
- Length \( l = 6 \frac{1}{8} \) ft
- Width \( w = 7 \frac{1}{4} \) ft
Step 1: Convert the mixed numbers to improper fractions.
-
Height: \[ 3 \frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5} \]
-
Length: \[ 6 \frac{1}{8} = \frac{6 \times 8 + 1}{8} = \frac{48 + 1}{8} = \frac{49}{8} \]
-
Width: \[ 7 \frac{1}{4} = \frac{7 \times 4 + 1}{4} = \frac{28 + 1}{4} = \frac{29}{4} \]
Step 2: Calculate the area of the base \( B \).
\[ B = l \times w = \frac{49}{8} \times \frac{29}{4} \]
Calculate \( B \):
\[ B = \frac{49 \times 29}{8 \times 4} = \frac{1421}{32} \]
Step 3: Calculate the volume \( V \).
\[ V = B \times h = \frac{1421}{32} \times \frac{17}{5} \]
Calculate \( V \):
\[ V = \frac{1421 \times 17}{32 \times 5} = \frac{24157}{160} \]
Step 4: Convert to a mixed number.
To convert \( \frac{24157}{160} \) to a mixed number:
- Perform the division \( 24157 \div 160 = 150 \) (the integer part)
- Calculate the remainder: \( 24157 - (150 \times 160) = 24157 - 24000 = 157 \)
So,
\[ \frac{24157}{160} = 150 \frac{157}{160} \]
Final answer:
The volume of the rectangular prism is:
\[ 150 \frac{157}{160} \text{ ft}^3 \]
Thus, the correct response is 150 157/160 ft.^3.