Question
Use the formula to determine the furface area of a right rectangular prism where each edge length measures 12.75 cm
459 cm^2
975.38 cm^2
5,852.25 cm^2
76.5 cm^2
459 cm^2
975.38 cm^2
5,852.25 cm^2
76.5 cm^2
Answers
Answer
you sure
Answered by
GPT-4o mini
To find the surface area of a right rectangular prism, you can use the formula:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where:
- \( l \) = length
- \( w \) = width
- \( h \) = height
Since all three edge lengths are equal (12.75 cm), we can consider it a cube, where \( l = w = h = 12.75 \) cm.
Now, insert the length, width, and height into the formula:
\[
\text{Surface Area} = 2(12.75 \times 12.75 + 12.75 \times 12.75 + 12.75 \times 12.75)
\]
Calculating \( 12.75 \times 12.75 \):
\[
12.75 \times 12.75 = 162.5625
\]
Now put that back into the surface area formula:
\[
\text{Surface Area} = 2(162.5625 + 162.5625 + 162.5625)
\]
\[
\text{Surface Area} = 2(3 \times 162.5625)
\]
\[
\text{Surface Area} = 2(487.6875) = 975.375
\]
So rounding, the surface area is approximately:
\[
\text{Surface Area} = 975.38 \text{ cm}^2.
\]
The correct answer from your provided options is **975.38 cm²**.
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where:
- \( l \) = length
- \( w \) = width
- \( h \) = height
Since all three edge lengths are equal (12.75 cm), we can consider it a cube, where \( l = w = h = 12.75 \) cm.
Now, insert the length, width, and height into the formula:
\[
\text{Surface Area} = 2(12.75 \times 12.75 + 12.75 \times 12.75 + 12.75 \times 12.75)
\]
Calculating \( 12.75 \times 12.75 \):
\[
12.75 \times 12.75 = 162.5625
\]
Now put that back into the surface area formula:
\[
\text{Surface Area} = 2(162.5625 + 162.5625 + 162.5625)
\]
\[
\text{Surface Area} = 2(3 \times 162.5625)
\]
\[
\text{Surface Area} = 2(487.6875) = 975.375
\]
So rounding, the surface area is approximately:
\[
\text{Surface Area} = 975.38 \text{ cm}^2.
\]
The correct answer from your provided options is **975.38 cm²**.
Answered by
GPT-4o mini
Yes, let's double-check the calculations for the surface area of a right rectangular prism (in this case, a cube since all sides are equal with edge lengths of 12.75 cm).
1. **Dimensions**:
- Length (\( l \)), Width (\( w \)), Height (\( h \)) = 12.75 cm each.
2. **Surface Area Formula**:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
3. **Calculating Each Area**:
- Since \( l = w = h = 12.75 \) cm:
\[
\text{Surface Area} = 2(12.75 \times 12.75 + 12.75 \times 12.75 + 12.75 \times 12.75)
\]
- Each product \( 12.75 \times 12.75 = 162.5625 \).
4. **Substituting Back**:
\[
\text{Surface Area} = 2(162.5625 + 162.5625 + 162.5625) = 2(3 \times 162.5625)
\]
\[
= 2(487.6875) = 975.375 \text{ cm}^2
\]
5. **Final Value**:
Rounding this value gives us \( 975.38 \text{ cm}^2 \).
Thus, my previous response was indeed correct, and the surface area of the right rectangular prism with edge lengths of 12.75 cm is \( 975.38 \text{ cm}^2 \). If you have any further queries or need assistance with different calculations, feel free to ask!
1. **Dimensions**:
- Length (\( l \)), Width (\( w \)), Height (\( h \)) = 12.75 cm each.
2. **Surface Area Formula**:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
3. **Calculating Each Area**:
- Since \( l = w = h = 12.75 \) cm:
\[
\text{Surface Area} = 2(12.75 \times 12.75 + 12.75 \times 12.75 + 12.75 \times 12.75)
\]
- Each product \( 12.75 \times 12.75 = 162.5625 \).
4. **Substituting Back**:
\[
\text{Surface Area} = 2(162.5625 + 162.5625 + 162.5625) = 2(3 \times 162.5625)
\]
\[
= 2(487.6875) = 975.375 \text{ cm}^2
\]
5. **Final Value**:
Rounding this value gives us \( 975.38 \text{ cm}^2 \).
Thus, my previous response was indeed correct, and the surface area of the right rectangular prism with edge lengths of 12.75 cm is \( 975.38 \text{ cm}^2 \). If you have any further queries or need assistance with different calculations, feel free to ask!
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