Question
What is the volume of a pasta box that is 2 1/2 in. long, 8 1/2 in. tall, and 1/2 in. wide? Apply the V=B×h formula to solve.(1 point)
Responses
1 1/4 in.^3
10 5/8in.^3
21 1/4in.^3
11 1/2in.^3
Responses
1 1/4 in.^3
10 5/8in.^3
21 1/4in.^3
11 1/2in.^3
Answers
GPT-4o mini
To find the volume \( V \) of the pasta box, we will use the formula \( V = B \times h \), where \( B \) is the area of the base and \( h \) is the height.
First, we determine the area of the base \( B \). The base is a rectangle with length \( 2 \frac{1}{2} \) inches and width \( \frac{1}{2} \) inches.
1. Convert \( 2 \frac{1}{2} \) to improper fraction:
\[
2 \frac{1}{2} = \frac{5}{2} \text{ inches}
\]
2. The width is \( \frac{1}{2} \) inches.
3. Calculate the area of the base \( B \):
\[
B = \text{length} \times \text{width} = \frac{5}{2} \times \frac{1}{2} = \frac{5}{4} \text{ square inches}
\]
Next, we multiply the area of the base \( B \) by the height \( h \):
1. The height is \( 8 \frac{1}{2} \) inches, which we convert to an improper fraction:
\[
8 \frac{1}{2} = \frac{17}{2} \text{ inches}
\]
2. Now, calculate the volume \( V \):
\[
V = B \times h = \frac{5}{4} \times \frac{17}{2}
\]
To multiply these fractions:
\[
V = \frac{5 \times 17}{4 \times 2} = \frac{85}{8} \text{ cubic inches}
\]
3. Convert \( \frac{85}{8} \) into a mixed number:
\[
85 \div 8 = 10 \text{ remainder } 5, \quad \text{so} \quad \frac{85}{8} = 10 \frac{5}{8} \text{ cubic inches}
\]
Thus, the volume of the pasta box is:
\[
\boxed{10 \frac{5}{8} \text{ in}^3}
\]
So, the correct response is **10 5/8 in.^3**.
First, we determine the area of the base \( B \). The base is a rectangle with length \( 2 \frac{1}{2} \) inches and width \( \frac{1}{2} \) inches.
1. Convert \( 2 \frac{1}{2} \) to improper fraction:
\[
2 \frac{1}{2} = \frac{5}{2} \text{ inches}
\]
2. The width is \( \frac{1}{2} \) inches.
3. Calculate the area of the base \( B \):
\[
B = \text{length} \times \text{width} = \frac{5}{2} \times \frac{1}{2} = \frac{5}{4} \text{ square inches}
\]
Next, we multiply the area of the base \( B \) by the height \( h \):
1. The height is \( 8 \frac{1}{2} \) inches, which we convert to an improper fraction:
\[
8 \frac{1}{2} = \frac{17}{2} \text{ inches}
\]
2. Now, calculate the volume \( V \):
\[
V = B \times h = \frac{5}{4} \times \frac{17}{2}
\]
To multiply these fractions:
\[
V = \frac{5 \times 17}{4 \times 2} = \frac{85}{8} \text{ cubic inches}
\]
3. Convert \( \frac{85}{8} \) into a mixed number:
\[
85 \div 8 = 10 \text{ remainder } 5, \quad \text{so} \quad \frac{85}{8} = 10 \frac{5}{8} \text{ cubic inches}
\]
Thus, the volume of the pasta box is:
\[
\boxed{10 \frac{5}{8} \text{ in}^3}
\]
So, the correct response is **10 5/8 in.^3**.