Question

Apply the formula V=B×h . What is the volume of a rectangular prism with a height of 3 2/5 ft., a length of 6 1/8 ft., and a width of 7 1/4 ft.?(1 point)

44 13/32ft^3
16 31/40ft^3
150 157/160ft^3
157 150/160ft^3

Answer 1

To calculate the volume \( V \) of a rectangular prism, we can use the formula:

\[
V = B \times h
\]

where \( B \) is the area of the base and \( h \) is the height.

The base \( B \) of the rectangular prism can be calculated as:

\[
B = \text{length} \times \text{width}
\]

Given:
- Height \( h = 3 \frac{2}{5} \) ft
- Length = \( 6 \frac{1}{8} \) ft
- Width = \( 7 \frac{1}{4} \) ft

### Step 1: Convert mixed numbers to improper fractions

1. **Height**:
\[
3 \frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5}
\]

2. **Length**:
\[
6 \frac{1}{8} = \frac{6 \times 8 + 1}{8} = \frac{48 + 1}{8} = \frac{49}{8}
\]

3. **Width**:
\[
7 \frac{1}{4} = \frac{7 \times 4 + 1}{4} = \frac{28 + 1}{4} = \frac{29}{4}
\]

### Step 2: Calculate the base area \( B \)

\[
B = \text{Length} \times \text{Width} = \frac{49}{8} \times \frac{29}{4}
\]

Calculating this gives:

\[
B = \frac{49 \cdot 29}{8 \cdot 4} = \frac{1421}{32}
\]

### Step 3: Calculate the volume \( V \)

Now we can plug \( B \) and \( h \) into the volume formula:

\[
V = B \times h = \frac{1421}{32} \times \frac{17}{5}
\]

Calculating this gives:

\[
V = \frac{1421 \cdot 17}{32 \cdot 5} = \frac{24157}{160}
\]

### Step 4: Convert to a mixed number

To convert \(\frac{24157}{160}\) into a mixed number:

1. Divide \( 24157 \) by \( 160 \):
\[
24157 \div 160 = 150 \quad \text{(whole part)}
\]

Remainder:
\[
24157 - (150 \times 160) = 24157 - 24000 = 157
\]

So we have:

\[
\frac{24157}{160} = 150 \frac{157}{160}
\]

### Final Answer

The volume of the rectangular prism is:

\[
\boxed{150 \frac{157}{160} \text{ ft}^3}
\]