Question
3. Find the surface area of a textbook that is 2 in. × 14 in. × 9 in.
2
in.
×
14
in.
×
9
in.
(1 point)
Responses
50 in.2
50
in.
2
50 in. squared
172 in.2
172
in.
2
172 in. squared
344 in.2
344
in.
2
344 in. squared
252 in.2
squared
2
in.
×
14
in.
×
9
in.
(1 point)
Responses
50 in.2
50
in.
2
50 in. squared
172 in.2
172
in.
2
172 in. squared
344 in.2
344
in.
2
344 in. squared
252 in.2
squared
Answers
GPT-4o mini
To find the surface area of a rectangular prism (like a textbook), you can use the formula:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where \( l \), \( w \), and \( h \) are the lengths of the sides of the prism.
For the textbook with dimensions 2 in. × 14 in. × 9 in.:
- \( l = 2 \) in.
- \( w = 14 \) in.
- \( h = 9 \) in.
Now, we calculate:
\[
lw = 2 \times 14 = 28 \, \text{in}^2
\]
\[
lh = 2 \times 9 = 18 \, \text{in}^2
\]
\[
wh = 14 \times 9 = 126 \, \text{in}^2
\]
Now, sum these areas:
\[
lw + lh + wh = 28 + 18 + 126 = 172 \, \text{in}^2
\]
Finally, plug this into the surface area formula:
\[
\text{Surface Area} = 2 \times 172 = 344 \, \text{in}^2
\]
So, the surface area of the textbook is \( 344 \, \text{in}^2 \).
The correct response is:
344 in.²
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where \( l \), \( w \), and \( h \) are the lengths of the sides of the prism.
For the textbook with dimensions 2 in. × 14 in. × 9 in.:
- \( l = 2 \) in.
- \( w = 14 \) in.
- \( h = 9 \) in.
Now, we calculate:
\[
lw = 2 \times 14 = 28 \, \text{in}^2
\]
\[
lh = 2 \times 9 = 18 \, \text{in}^2
\]
\[
wh = 14 \times 9 = 126 \, \text{in}^2
\]
Now, sum these areas:
\[
lw + lh + wh = 28 + 18 + 126 = 172 \, \text{in}^2
\]
Finally, plug this into the surface area formula:
\[
\text{Surface Area} = 2 \times 172 = 344 \, \text{in}^2
\]
So, the surface area of the textbook is \( 344 \, \text{in}^2 \).
The correct response is:
344 in.²