Question
Apply the formula V = B x h. What is the volume of a rectangular prism with a height of 3 2/5 ft., a length of 61/8 ft ., and a width of 7 1/4 ft.?
A. 150 157/160ft^3
B. 44 13/32 ft^3
C. 157 150/160 ft^3
D. 16 31/40 ft^3
A. 150 157/160ft^3
B. 44 13/32 ft^3
C. 157 150/160 ft^3
D. 16 31/40 ft^3
Answers
Answered by
GPT-4o mini
To find the volume \( V \) of a rectangular prism using the formula \( V = B \times h \), where \( B \) is the area of the base and \( h \) is the height, we first need to calculate the area of the base \( B \), which is \( l \times w \) (length times width).
Let's define the dimensions 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 mixed numbers into improper fractions.**
1. For the height \( h \):
\[
h = 3 \frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5}
\]
2. For the length \( l \):
\[
l = 6 \frac{1}{8} = \frac{6 \times 8 + 1}{8} = \frac{48 + 1}{8} = \frac{49}{8}
\]
3. For the width \( w \):
\[
w = 7 \frac{1}{4} = \frac{7 \times 4 + 1}{4} = \frac{28 + 1}{4} = \frac{29}{4}
\]
**Step 2: Calculate the area of the base \( B \).**
\[
B = l \times w = \left( \frac{49}{8} \times \frac{29}{4} \right)
\]
Now, multiply the fractions:
\[
B = \frac{49 \times 29}{8 \times 4} = \frac{1421}{32}
\]
**Step 3: Calculate the volume \( V \) using the height.**
\[
V = B \times h = \left( \frac{1421}{32} \times \frac{17}{5} \right)
\]
\[
V = \frac{1421 \times 17}{32 \times 5} = \frac{24157}{160}
\]
**Step 4: Convert the improper fraction to a mixed number.**
To convert \( \frac{24157}{160} \) to a mixed number:
1. Divide 24157 by 160.
2. Find the whole number part and the remainder.
\[
24157 \div 160 \approx 150.98 \quad \text{(which gives us 150 as the whole number part)}
\]
3. Calculate the remaining part:
\[
24157 - (150 \times 160) = 24157 - 24000 = 157
\]
So, the mixed number is:
\[
150 \frac{157}{160}
\]
Thus, the volume of the rectangular prism is \( 150 \frac{157}{160} \) ft³.
**Final Answer:**
The correct option is **A. \( 150 \frac{157}{160} \) ft³**.
Let's define the dimensions 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 mixed numbers into improper fractions.**
1. For the height \( h \):
\[
h = 3 \frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5}
\]
2. For the length \( l \):
\[
l = 6 \frac{1}{8} = \frac{6 \times 8 + 1}{8} = \frac{48 + 1}{8} = \frac{49}{8}
\]
3. For the width \( w \):
\[
w = 7 \frac{1}{4} = \frac{7 \times 4 + 1}{4} = \frac{28 + 1}{4} = \frac{29}{4}
\]
**Step 2: Calculate the area of the base \( B \).**
\[
B = l \times w = \left( \frac{49}{8} \times \frac{29}{4} \right)
\]
Now, multiply the fractions:
\[
B = \frac{49 \times 29}{8 \times 4} = \frac{1421}{32}
\]
**Step 3: Calculate the volume \( V \) using the height.**
\[
V = B \times h = \left( \frac{1421}{32} \times \frac{17}{5} \right)
\]
\[
V = \frac{1421 \times 17}{32 \times 5} = \frac{24157}{160}
\]
**Step 4: Convert the improper fraction to a mixed number.**
To convert \( \frac{24157}{160} \) to a mixed number:
1. Divide 24157 by 160.
2. Find the whole number part and the remainder.
\[
24157 \div 160 \approx 150.98 \quad \text{(which gives us 150 as the whole number part)}
\]
3. Calculate the remaining part:
\[
24157 - (150 \times 160) = 24157 - 24000 = 157
\]
So, the mixed number is:
\[
150 \frac{157}{160}
\]
Thus, the volume of the rectangular prism is \( 150 \frac{157}{160} \) ft³.
**Final Answer:**
The correct option is **A. \( 150 \frac{157}{160} \) ft³**.
Answered by
.
Yeah the bot is right