Question
1. Explain how to find the Volume of the rectangular prism above. Show all steps! (2 points)
the h is 3.5 in
the w is 1 in
and the l is 5in
2. Explain how to find the Surface Area of the rectangular prism above. Show all steps! (2 points)
(4 points)
0 / 10000 Word Limit
Question 2
If you wanted to know how much water this rectangular prism could hold inside of it, which measurement would you use?(1 point)
Responses
volume
volume
surface area
the h is 3.5 in
the w is 1 in
and the l is 5in
2. Explain how to find the Surface Area of the rectangular prism above. Show all steps! (2 points)
(4 points)
0 / 10000 Word Limit
Question 2
If you wanted to know how much water this rectangular prism could hold inside of it, which measurement would you use?(1 point)
Responses
volume
volume
surface area
Answers
GPT-4o mini
### 1. Finding the Volume of the Rectangular Prism
To find the volume of a rectangular prism, you use the formula:
\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]
**Step 1:** Identify the dimensions of the prism.
- Height (h) = 3.5 inches
- Width (w) = 1 inch
- Length (l) = 5 inches
**Step 2:** Substitute the values into the volume formula.
\[
\text{Volume} = l \times w \times h = 5 \, \text{in} \times 1 \, \text{in} \times 3.5 \, \text{in}
\]
**Step 3:** Perform the multiplication.
\[
\text{Volume} = 5 \times 1 \times 3.5 = 5 \times 3.5 = 17.5 \, \text{cubic inches}
\]
So, the volume of the rectangular prism is **17.5 cubic inches**.
---
### 2. Finding the Surface Area of the Rectangular Prism
To find the surface area of a rectangular prism, you use the formula:
\[
\text{Surface Area} = 2lw + 2lh + 2wh
\]
**Step 1:** Identify the dimensions of the prism again.
- Height (h) = 3.5 inches
- Width (w) = 1 inch
- Length (l) = 5 inches
**Step 2:** Substitute the values into the surface area formula.
\[
\text{Surface Area} = 2(lw) + 2(lh) + 2(wh)
\]
**Step 3:** Calculate each term separately.
1. **Calculate \(2lw\)**:
\[
2lw = 2 \times 5 \times 1 = 10 \, \text{square inches}
\]
2. **Calculate \(2lh\)**:
\[
2lh = 2 \times 5 \times 3.5 = 35 \, \text{square inches}
\]
3. **Calculate \(2wh\)**:
\[
2wh = 2 \times 1 \times 3.5 = 7 \, \text{square inches}
\]
**Step 4:** Add the areas of all faces to find the total surface area.
\[
\text{Surface Area} = 10 + 35 + 7 = 52 \, \text{square inches}
\]
So, the surface area of the rectangular prism is **52 square inches**.
---
### Question 2: Measurement for Water Capacity
If you wanted to know how much water this rectangular prism could hold inside of it, you would use the **volume** measurement. The volume tells you the amount of space inside the prism, which corresponds to how much liquid it can contain.
The correct response is:
**volume**
To find the volume of a rectangular prism, you use the formula:
\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]
**Step 1:** Identify the dimensions of the prism.
- Height (h) = 3.5 inches
- Width (w) = 1 inch
- Length (l) = 5 inches
**Step 2:** Substitute the values into the volume formula.
\[
\text{Volume} = l \times w \times h = 5 \, \text{in} \times 1 \, \text{in} \times 3.5 \, \text{in}
\]
**Step 3:** Perform the multiplication.
\[
\text{Volume} = 5 \times 1 \times 3.5 = 5 \times 3.5 = 17.5 \, \text{cubic inches}
\]
So, the volume of the rectangular prism is **17.5 cubic inches**.
---
### 2. Finding the Surface Area of the Rectangular Prism
To find the surface area of a rectangular prism, you use the formula:
\[
\text{Surface Area} = 2lw + 2lh + 2wh
\]
**Step 1:** Identify the dimensions of the prism again.
- Height (h) = 3.5 inches
- Width (w) = 1 inch
- Length (l) = 5 inches
**Step 2:** Substitute the values into the surface area formula.
\[
\text{Surface Area} = 2(lw) + 2(lh) + 2(wh)
\]
**Step 3:** Calculate each term separately.
1. **Calculate \(2lw\)**:
\[
2lw = 2 \times 5 \times 1 = 10 \, \text{square inches}
\]
2. **Calculate \(2lh\)**:
\[
2lh = 2 \times 5 \times 3.5 = 35 \, \text{square inches}
\]
3. **Calculate \(2wh\)**:
\[
2wh = 2 \times 1 \times 3.5 = 7 \, \text{square inches}
\]
**Step 4:** Add the areas of all faces to find the total surface area.
\[
\text{Surface Area} = 10 + 35 + 7 = 52 \, \text{square inches}
\]
So, the surface area of the rectangular prism is **52 square inches**.
---
### Question 2: Measurement for Water Capacity
If you wanted to know how much water this rectangular prism could hold inside of it, you would use the **volume** measurement. The volume tells you the amount of space inside the prism, which corresponds to how much liquid it can contain.
The correct response is:
**volume**