Question
A carry-on suitcase is 9.5 inches long, 16 inches wide, and 22.5 inches high. What is the surface area of the suitcase?
*Hint: Don't forget to use your Desmos calculator and STAAR Reference Sheet to help!
(1 point)
Responses
96 in.2
96 in.2
1,451.5 in.2
1,451.5 in.2
3,420 in.2
3,420 in.2
725.75 in.2
You need to paint the side walls of your bedroom. If the room is 12 feet by 14 feet, and it has a ceiling 10 feet high. What is the area you need to paint?
*Hint: Don't forget to use your Desmos calculator and STAAR Reference Sheet to help!
(1 point)
Responses
96 in.2
96 in.2
1,451.5 in.2
1,451.5 in.2
3,420 in.2
3,420 in.2
725.75 in.2
You need to paint the side walls of your bedroom. If the room is 12 feet by 14 feet, and it has a ceiling 10 feet high. What is the area you need to paint?
Answers
Answered by
GPT-4o mini
To find the surface area of the carry-on suitcase, we can use the formula for the surface area of a rectangular prism:
\[
\text{Surface Area} = 2lw + 2lh + 2wh
\]
Where:
- \( l \) = length
- \( w \) = width
- \( h \) = height
Given:
- \( l = 9.5 \) inches
- \( w = 16 \) inches
- \( h = 22.5 \) inches
Now, let's calculate each part of the surface area:
1. \( 2lw = 2 \times 9.5 \times 16 = 304 \)
2. \( 2lh = 2 \times 9.5 \times 22.5 = 427.5 \)
3. \( 2wh = 2 \times 16 \times 22.5 = 720 \)
Now we add these up:
\[
\text{Surface Area} = 304 + 427.5 + 720 = 1451.5 \text{ in}^2
\]
Thus, the surface area of the suitcase is **1,451.5 in²**.
---
Now let's calculate the area you need to paint in your bedroom.
The room is a rectangle with the following dimensions:
- Length = 14 feet
- Width = 12 feet
- Height = 10 feet
The area of the walls is calculated as follows:
1. Two walls will have a height of 10 feet and a length of 14 feet:
- Area of the two longer walls = \( 2 \times (14 \times 10) = 280 \text{ ft}^2 \)
2. Two walls will have a height of 10 feet and a width of 12 feet:
- Area of the two shorter walls = \( 2 \times (12 \times 10) = 240 \text{ ft}^2 \)
Now, we add these areas together:
\[
\text{Total Area to Paint} = 280 + 240 = 520 \text{ ft}^2
\]
Thus, the area you need to paint is **520 ft²**.
\[
\text{Surface Area} = 2lw + 2lh + 2wh
\]
Where:
- \( l \) = length
- \( w \) = width
- \( h \) = height
Given:
- \( l = 9.5 \) inches
- \( w = 16 \) inches
- \( h = 22.5 \) inches
Now, let's calculate each part of the surface area:
1. \( 2lw = 2 \times 9.5 \times 16 = 304 \)
2. \( 2lh = 2 \times 9.5 \times 22.5 = 427.5 \)
3. \( 2wh = 2 \times 16 \times 22.5 = 720 \)
Now we add these up:
\[
\text{Surface Area} = 304 + 427.5 + 720 = 1451.5 \text{ in}^2
\]
Thus, the surface area of the suitcase is **1,451.5 in²**.
---
Now let's calculate the area you need to paint in your bedroom.
The room is a rectangle with the following dimensions:
- Length = 14 feet
- Width = 12 feet
- Height = 10 feet
The area of the walls is calculated as follows:
1. Two walls will have a height of 10 feet and a length of 14 feet:
- Area of the two longer walls = \( 2 \times (14 \times 10) = 280 \text{ ft}^2 \)
2. Two walls will have a height of 10 feet and a width of 12 feet:
- Area of the two shorter walls = \( 2 \times (12 \times 10) = 240 \text{ ft}^2 \)
Now, we add these areas together:
\[
\text{Total Area to Paint} = 280 + 240 = 520 \text{ ft}^2
\]
Thus, the area you need to paint is **520 ft²**.