Question
If the length is 8 inches, the width is 7 inches, and the height is 24 inches, what is the surface area of the rectangular prism?
A.
1,344 in2
B.
922 in2
C.
742 in2
D.
832 in2
Answers
GPT-4o mini
To find the surface area of a rectangular prism, you can use the formula:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
Given:
- \( l = 8 \) inches
- \( w = 7 \) inches
- \( h = 24 \) inches
First, calculate the products inside the parentheses:
1. \( lw = 8 \times 7 = 56 \)
2. \( lh = 8 \times 24 = 192 \)
3. \( wh = 7 \times 24 = 168 \)
Now sum these products:
\[
lw + lh + wh = 56 + 192 + 168 = 416
\]
Now, multiply by 2 to find the surface area:
\[
\text{Surface Area} = 2 \times 416 = 832 \, \text{in}^2
\]
So, the surface area of the rectangular prism is:
\[
\boxed{832 \, \text{in}^2}
\]
Thus, the answer is \( D. \, 832 \, \text{in}^2 \).
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
Given:
- \( l = 8 \) inches
- \( w = 7 \) inches
- \( h = 24 \) inches
First, calculate the products inside the parentheses:
1. \( lw = 8 \times 7 = 56 \)
2. \( lh = 8 \times 24 = 192 \)
3. \( wh = 7 \times 24 = 168 \)
Now sum these products:
\[
lw + lh + wh = 56 + 192 + 168 = 416
\]
Now, multiply by 2 to find the surface area:
\[
\text{Surface Area} = 2 \times 416 = 832 \, \text{in}^2
\]
So, the surface area of the rectangular prism is:
\[
\boxed{832 \, \text{in}^2}
\]
Thus, the answer is \( D. \, 832 \, \text{in}^2 \).