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)
Responses

16 31/40ft.^3

44 13/32ft.^3

157 150/160ft.^3

150 157/160ft.^3

Answer 1

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.**

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 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**.