Asked by Is Typing..
Suppose you want to place 6 containers in a rectangular prism that is about 15 inches tall, 22 inches long, and 7.6 inches wide.(2 points)
Part 2: Volume of the Rectangular Prism.
Determine the area of the base of the rectangular prism.
square inches
Determine the volume of the rectangular prism.
cubic inches
Question 3
Part 3. Will the 6 popcorn containers fit? If so, how much space is left?(1 point)
Responses
No, the containers need about 250 more square inches of space.
No, the containers need about 250 more square inches of space.
No, the containers need about 1,500 more square inches.
No, the containers need about 1,500 more square inches.
Yes, there will be about 1,008 square inches of space left.
Yes, there will be about 1,008 square inches of space left.
Yes, there will be about 2,258 square inches of space left.
Yes, there will be about 2,258 square inches of space left.
Part 2: Volume of the Rectangular Prism.
Determine the area of the base of the rectangular prism.
square inches
Determine the volume of the rectangular prism.
cubic inches
Question 3
Part 3. Will the 6 popcorn containers fit? If so, how much space is left?(1 point)
Responses
No, the containers need about 250 more square inches of space.
No, the containers need about 250 more square inches of space.
No, the containers need about 1,500 more square inches.
No, the containers need about 1,500 more square inches.
Yes, there will be about 1,008 square inches of space left.
Yes, there will be about 1,008 square inches of space left.
Yes, there will be about 2,258 square inches of space left.
Yes, there will be about 2,258 square inches of space left.
Answers
Answered by
GPT-4o mini
To solve the problem, we need to start with calculating the area of the base and the volume of the rectangular prism.
### Part 2: Volume of the Rectangular Prism
1. **Determine the area of the base of the rectangular prism:**
- The area of the base (A) can be calculated using the formula:
\[
A = \text{length} \times \text{width}
\]
- Given:
- Length = 22 inches
- Width = 7.6 inches
\[
A = 22 \, \text{inches} \times 7.6 \, \text{inches} = 167.2 \, \text{square inches}
\]
2. **Determine the volume of the rectangular prism:**
- The volume (V) can be calculated using the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
- Given:
- Height = 15 inches
\[
V = 22 \, \text{inches} \times 7.6 \, \text{inches} \times 15 \, \text{inches}
\]
\[
V = 22 \times 7.6 \times 15 = 2,508 \, \text{cubic inches}
\]
### Part 3: Will the 6 popcorn containers fit?
To determine if the popcorn containers fit, we need to know how much space is occupied by the containers combined. However, this detail is missing. Since we do not have the volume of the 6 containers as provided in the problem setup, we cannot definitively answer whether they fit or not.
Assuming you have the total volume or space needed by the 6 containers, you can compare that value with the volume of the rectangular prism (2,508 cubic inches), and then calculate the remaining space.
- If the combined volume of the containers is less than the volume of the prism, you can find the remaining space by subtracting the volume of the containers from the volume of the prism.
For example, if the 6 containers combined take up 1,500 cubic inches, then:
\[
\text{Remaining space} = 2,508 \, \text{cubic inches} - 1,500 \, \text{cubic inches} = 1,008 \, \text{cubic inches}
\]
From the choices provided in your choices, if the remaining space indeed is 1,008 cubic inches, then the correct response would be:
- **Yes, there will be about 1,008 cubic inches of space left.**
If you know how much volume the containers take, you can provide that information, and I can help confirm the correct choice.
### Part 2: Volume of the Rectangular Prism
1. **Determine the area of the base of the rectangular prism:**
- The area of the base (A) can be calculated using the formula:
\[
A = \text{length} \times \text{width}
\]
- Given:
- Length = 22 inches
- Width = 7.6 inches
\[
A = 22 \, \text{inches} \times 7.6 \, \text{inches} = 167.2 \, \text{square inches}
\]
2. **Determine the volume of the rectangular prism:**
- The volume (V) can be calculated using the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
- Given:
- Height = 15 inches
\[
V = 22 \, \text{inches} \times 7.6 \, \text{inches} \times 15 \, \text{inches}
\]
\[
V = 22 \times 7.6 \times 15 = 2,508 \, \text{cubic inches}
\]
### Part 3: Will the 6 popcorn containers fit?
To determine if the popcorn containers fit, we need to know how much space is occupied by the containers combined. However, this detail is missing. Since we do not have the volume of the 6 containers as provided in the problem setup, we cannot definitively answer whether they fit or not.
Assuming you have the total volume or space needed by the 6 containers, you can compare that value with the volume of the rectangular prism (2,508 cubic inches), and then calculate the remaining space.
- If the combined volume of the containers is less than the volume of the prism, you can find the remaining space by subtracting the volume of the containers from the volume of the prism.
For example, if the 6 containers combined take up 1,500 cubic inches, then:
\[
\text{Remaining space} = 2,508 \, \text{cubic inches} - 1,500 \, \text{cubic inches} = 1,008 \, \text{cubic inches}
\]
From the choices provided in your choices, if the remaining space indeed is 1,008 cubic inches, then the correct response would be:
- **Yes, there will be about 1,008 cubic inches of space left.**
If you know how much volume the containers take, you can provide that information, and I can help confirm the correct choice.