Question
What is the surface area of a rectangular prism where each edge length measures 15.1 cm?
(1 point)
Responses
1,350 cm2
1,350 cm2
900 cm2
900 cm 2
1,368.06 cm2
1,368.06 cm 2
8,208.36 cm2
(1 point)
Responses
1,350 cm2
1,350 cm2
900 cm2
900 cm 2
1,368.06 cm2
1,368.06 cm 2
8,208.36 cm2
Answers
GPT-4o mini
To find the surface area of a rectangular prism, we can use the formula:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where \( l \), \( w \), and \( h \) are the lengths of the edges of the prism. In this case, since each edge length measures 15.1 cm, we have \( l = w = h = 15.1 \) cm.
Now we can calculate:
\[
lw = 15.1 \times 15.1 = 228.01 \, \text{cm}^2
\]
\[
lh = 15.1 \times 15.1 = 228.01 \, \text{cm}^2
\]
\[
wh = 15.1 \times 15.1 = 228.01 \, \text{cm}^2
\]
Now we combine these values:
\[
lw + lh + wh = 228.01 + 228.01 + 228.01 = 684.03 \, \text{cm}^2
\]
Next, we multiply this sum by 2 to find the total surface area:
\[
\text{Surface Area} = 2 \times 684.03 = 1368.06 \, \text{cm}^2
\]
Therefore, the surface area of the rectangular prism is **1,368.06 cm²**.
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where \( l \), \( w \), and \( h \) are the lengths of the edges of the prism. In this case, since each edge length measures 15.1 cm, we have \( l = w = h = 15.1 \) cm.
Now we can calculate:
\[
lw = 15.1 \times 15.1 = 228.01 \, \text{cm}^2
\]
\[
lh = 15.1 \times 15.1 = 228.01 \, \text{cm}^2
\]
\[
wh = 15.1 \times 15.1 = 228.01 \, \text{cm}^2
\]
Now we combine these values:
\[
lw + lh + wh = 228.01 + 228.01 + 228.01 = 684.03 \, \text{cm}^2
\]
Next, we multiply this sum by 2 to find the total surface area:
\[
\text{Surface Area} = 2 \times 684.03 = 1368.06 \, \text{cm}^2
\]
Therefore, the surface area of the rectangular prism is **1,368.06 cm²**.