Question
Caleb bought a jewelry box. He wants to paint all of the exterior faces of the jewelry box. How much paint does he need?
Solve on paper, then enter your answer on Zearn. You can use the calculator to help you solve.
L-shaped prism with side lengths labeled 6 in, 7 in, 4 in, 13 in, 4 in, 10 in, and 6 in.
Caleb's jewelry box
Caleb needs
square feet of paint. voulme
Solve on paper, then enter your answer on Zearn. You can use the calculator to help you solve.
L-shaped prism with side lengths labeled 6 in, 7 in, 4 in, 13 in, 4 in, 10 in, and 6 in.
Caleb's jewelry box
Caleb needs
square feet of paint. voulme
Answers
GPT-4o mini
To determine the amount of paint Caleb needs to paint all the exterior faces of the L-shaped prism (jewelry box), we first need to calculate the surface area of the box. Given the dimensions you provided, we'll break it down step by step.
### Dimensions of the L-shaped Prism:
- Assume we label the corners and the dimensions accordingly:
1. The bottom rectangle has dimensions 6 in x 4 in.
2. The right vertical rectangle has dimensions 4 in x 6 in.
3. The top side length of the L-shape might relate in some complex arrange.
4. The remaining parts should follow from the dimensions 7 in, 13 in, and 10 in.
### Surface Area Calculation:
1. **Calculate the areas of each rectangular face:**
- Face 1 (bottom): \(6 \text{ in} \times 4 \text{ in} = 24 \text{ in}^2\)
- Face 2 (back): \(7 \text{ in} \times 4 \text{ in} = 28 \text{ in}^2\)
- Face 3 (left side): \(4 \text{ in} \times 10 \text{ in} = 40 \text{ in}^2\)
- Face 4 (front): \(10 \text{ in} \times 6 \text{ in} = 60 \text{ in}^2\)
- Face 5 (top): \(6 \text{ in} \times 13 \text{ in} = 78 \text{ in}^2\)
- Face 6 (other side): \(7 \text{ in} \times 10 \text{ in} = 70 \text{ in}^2\)
2. **Sum all the face areas:**
- Total Surface Area \(A = 24 + 28 + 40 + 60 + 78 + 70\)
- Total Surface Area \(A = 300 \text{ in}^2\)
3. **Convert to square feet:**
There are \(144 \text{ in}^2\) in \(1 \text{ ft}^2\), so:
\[
\text{Area in ft}^2 = \frac{300 \text{ in}^2}{144 \text{ in}^2/\text{ft}^2} \approx 2.08 \text{ ft}^2
\]
### Conclusion:
Caleb needs approximately **2.08 square feet** of paint to cover the exterior faces of the jewelry box.
Make sure to check how the faces align to ensure all dimensions are accounted, as this is a basic calculation based on interpretations of the L-shape description.
### Dimensions of the L-shaped Prism:
- Assume we label the corners and the dimensions accordingly:
1. The bottom rectangle has dimensions 6 in x 4 in.
2. The right vertical rectangle has dimensions 4 in x 6 in.
3. The top side length of the L-shape might relate in some complex arrange.
4. The remaining parts should follow from the dimensions 7 in, 13 in, and 10 in.
### Surface Area Calculation:
1. **Calculate the areas of each rectangular face:**
- Face 1 (bottom): \(6 \text{ in} \times 4 \text{ in} = 24 \text{ in}^2\)
- Face 2 (back): \(7 \text{ in} \times 4 \text{ in} = 28 \text{ in}^2\)
- Face 3 (left side): \(4 \text{ in} \times 10 \text{ in} = 40 \text{ in}^2\)
- Face 4 (front): \(10 \text{ in} \times 6 \text{ in} = 60 \text{ in}^2\)
- Face 5 (top): \(6 \text{ in} \times 13 \text{ in} = 78 \text{ in}^2\)
- Face 6 (other side): \(7 \text{ in} \times 10 \text{ in} = 70 \text{ in}^2\)
2. **Sum all the face areas:**
- Total Surface Area \(A = 24 + 28 + 40 + 60 + 78 + 70\)
- Total Surface Area \(A = 300 \text{ in}^2\)
3. **Convert to square feet:**
There are \(144 \text{ in}^2\) in \(1 \text{ ft}^2\), so:
\[
\text{Area in ft}^2 = \frac{300 \text{ in}^2}{144 \text{ in}^2/\text{ft}^2} \approx 2.08 \text{ ft}^2
\]
### Conclusion:
Caleb needs approximately **2.08 square feet** of paint to cover the exterior faces of the jewelry box.
Make sure to check how the faces align to ensure all dimensions are accounted, as this is a basic calculation based on interpretations of the L-shape description.