Question
Calculate the surface area of a cube with 12-inch edges. How many square inches is the surface area?(1 point)
Caroline needs to find the surface area of a cereal box for an art project. The box is a rectangular prism with a length of 8 inches, a height of 12 inches, and a width of 2 inches. What is its surface area?(1 point)
A roll of wrapping paper measures 25 in.×405 in.
The boxes being wrapped are 16 in.×14 in.×6 in.
How many complete boxes can be wrapped with one roll of wrapping paper?(1 point)
What is the total surface area of a cube that has 8-inch sides?(1 point)
Caroline needs to find the surface area of a cereal box for an art project. The box is a rectangular prism with a length of 8 inches, a height of 12 inches, and a width of 2 inches. What is its surface area?(1 point)
A roll of wrapping paper measures 25 in.×405 in.
The boxes being wrapped are 16 in.×14 in.×6 in.
How many complete boxes can be wrapped with one roll of wrapping paper?(1 point)
What is the total surface area of a cube that has 8-inch sides?(1 point)
Answers
GPT-4o mini
### Calculation of Surface Area of a Cube
1. **Surface Area of a Cube with 12-inch Edges**
- Formula for surface area of a cube: \( SA = 6s^2 \)
- Where \( s \) is the length of one side of the cube.
- For a cube with edges of 12 inches:
\[
SA = 6 \times (12)^2 = 6 \times 144 = 864 \text{ square inches}
\]
- **Answer:** 864 square inches
---
### Calculation of Surface Area of a Rectangular Prism
2. **Surface Area of the Cereal Box (Rectangular Prism)**
- Length (l) = 8 inches, Width (w) = 2 inches, Height (h) = 12 inches.
- Formula for surface area of a rectangular prism:
\[
SA = 2(lw + lh + wh)
\]
- Calculating each term:
- \( lw = 8 \times 2 = 16 \)
- \( lh = 8 \times 12 = 96 \)
- \( wh = 2 \times 12 = 24 \)
- Sum them up:
\[
SA = 2(16 + 96 + 24) = 2(136) = 272 \text{ square inches}
\]
- **Answer:** 272 square inches
---
### Calculation of Number of Boxes Wrapped with a Roll of Wrapping Paper
3. **Wrapping Paper and Boxes**
- Size of the roll: 25 in. × 405 in. (which gives a total area of \( 25 \times 405 \)).
\[
\text{Area of the roll} = 25 \times 405 = 10125 \text{ square inches}
\]
- Size of one box: 16 in. × 14 in. × 6 in. (need to find the surface area).
- Surface area of one box:
\[
SA = 2(lw + lh + wh) = 2(16 \times 14 + 16 \times 6 + 14 \times 6)
\]
- Calculate each multiplication:
- \( lw = 16 \times 14 = 224 \)
- \( lh = 16 \times 6 = 96 \)
- \( wh = 14 \times 6 = 84 \)
- Adding them up:
\[
SA = 2(224 + 96 + 84) = 2(404) = 808 \text{ square inches}
\]
- Number of complete boxes that can be wrapped:
\[
\text{Number of boxes} = \frac{\text{Area of the roll}}{\text{Area of one box}} = \frac{10125}{808} \approx 12.5
\]
- Therefore, the maximum number of complete boxes = 12.
- **Answer:** 12 boxes
---
### Calculation of Total Surface Area of Another Cube
4. **Surface Area of a Cube with 8-inch Sides**
- For a cube with edges of 8 inches:
\[
SA = 6 \times (8)^2 = 6 \times 64 = 384 \text{ square inches}
\]
- **Answer:** 384 square inches
---
### Summary of Answers
1. **Surface area of the cube with 12-inch edges:** 864 square inches
2. **Surface area of the cereal box:** 272 square inches
3. **Number of complete boxes wrapped:** 12 boxes
4. **Surface area of the cube with 8-inch sides:** 384 square inches
1. **Surface Area of a Cube with 12-inch Edges**
- Formula for surface area of a cube: \( SA = 6s^2 \)
- Where \( s \) is the length of one side of the cube.
- For a cube with edges of 12 inches:
\[
SA = 6 \times (12)^2 = 6 \times 144 = 864 \text{ square inches}
\]
- **Answer:** 864 square inches
---
### Calculation of Surface Area of a Rectangular Prism
2. **Surface Area of the Cereal Box (Rectangular Prism)**
- Length (l) = 8 inches, Width (w) = 2 inches, Height (h) = 12 inches.
- Formula for surface area of a rectangular prism:
\[
SA = 2(lw + lh + wh)
\]
- Calculating each term:
- \( lw = 8 \times 2 = 16 \)
- \( lh = 8 \times 12 = 96 \)
- \( wh = 2 \times 12 = 24 \)
- Sum them up:
\[
SA = 2(16 + 96 + 24) = 2(136) = 272 \text{ square inches}
\]
- **Answer:** 272 square inches
---
### Calculation of Number of Boxes Wrapped with a Roll of Wrapping Paper
3. **Wrapping Paper and Boxes**
- Size of the roll: 25 in. × 405 in. (which gives a total area of \( 25 \times 405 \)).
\[
\text{Area of the roll} = 25 \times 405 = 10125 \text{ square inches}
\]
- Size of one box: 16 in. × 14 in. × 6 in. (need to find the surface area).
- Surface area of one box:
\[
SA = 2(lw + lh + wh) = 2(16 \times 14 + 16 \times 6 + 14 \times 6)
\]
- Calculate each multiplication:
- \( lw = 16 \times 14 = 224 \)
- \( lh = 16 \times 6 = 96 \)
- \( wh = 14 \times 6 = 84 \)
- Adding them up:
\[
SA = 2(224 + 96 + 84) = 2(404) = 808 \text{ square inches}
\]
- Number of complete boxes that can be wrapped:
\[
\text{Number of boxes} = \frac{\text{Area of the roll}}{\text{Area of one box}} = \frac{10125}{808} \approx 12.5
\]
- Therefore, the maximum number of complete boxes = 12.
- **Answer:** 12 boxes
---
### Calculation of Total Surface Area of Another Cube
4. **Surface Area of a Cube with 8-inch Sides**
- For a cube with edges of 8 inches:
\[
SA = 6 \times (8)^2 = 6 \times 64 = 384 \text{ square inches}
\]
- **Answer:** 384 square inches
---
### Summary of Answers
1. **Surface area of the cube with 12-inch edges:** 864 square inches
2. **Surface area of the cereal box:** 272 square inches
3. **Number of complete boxes wrapped:** 12 boxes
4. **Surface area of the cube with 8-inch sides:** 384 square inches