Question
Find the surface area of a box with a length of 2 cm, a width of 5 cm, and a height of 9 cm.
73 cm2
90 cm2
146 cm2
60 cm2
Answers
GPT-4o mini
The surface area \( S \) of a box (rectangular prism) can be calculated using the formula:
\[
S = 2(lw + lh + wh)
\]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given:
- Length \( l = 2 \) cm,
- Width \( w = 5 \) cm,
- Height \( h = 9 \) cm.
We can substitute the values into the formula:
1. Calculate \( lw \):
\[
lw = 2 \times 5 = 10 \, \text{cm}^2
\]
2. Calculate \( lh \):
\[
lh = 2 \times 9 = 18 \, \text{cm}^2
\]
3. Calculate \( wh \):
\[
wh = 5 \times 9 = 45 \, \text{cm}^2
\]
Now, we can sum these areas:
\[
lw + lh + wh = 10 + 18 + 45 = 73 \, \text{cm}^2
\]
Finally, multiply by 2 to find the total surface area:
\[
S = 2(73) = 146 \, \text{cm}^2
\]
So, the surface area of the box is **146 cm²**.
\[
S = 2(lw + lh + wh)
\]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given:
- Length \( l = 2 \) cm,
- Width \( w = 5 \) cm,
- Height \( h = 9 \) cm.
We can substitute the values into the formula:
1. Calculate \( lw \):
\[
lw = 2 \times 5 = 10 \, \text{cm}^2
\]
2. Calculate \( lh \):
\[
lh = 2 \times 9 = 18 \, \text{cm}^2
\]
3. Calculate \( wh \):
\[
wh = 5 \times 9 = 45 \, \text{cm}^2
\]
Now, we can sum these areas:
\[
lw + lh + wh = 10 + 18 + 45 = 73 \, \text{cm}^2
\]
Finally, multiply by 2 to find the total surface area:
\[
S = 2(73) = 146 \, \text{cm}^2
\]
So, the surface area of the box is **146 cm²**.