Question
The surface area of an open-top box with length \( L \), width \( W \), and height \( H \) can be found using the formula: \( A=2 L H+2 W H+L W \) Find the surface area of an open-top box with length 9 cm , width 6 cm , and height 7 cm .
Ask by Ayala Wright. in the United States
Mar 16,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The surface area of the open-top box is 264 cm².
Solution
Given the formula for the surface area of an open-top box:
\[
A = 2LH + 2WH + LW
\]
we substitute \( L = 9 \) cm, \( W = 6 \) cm, and \( H = 7 \) cm.
1. Calculate \( 2LH \):
\[
2LH = 2(9)(7) = 2(63) = 126 \text{ cm}^2
\]
2. Calculate \( 2WH \):
\[
2WH = 2(6)(7) = 2(42) = 84 \text{ cm}^2
\]
3. Calculate \( LW \):
\[
LW = 9 \times 6 = 54 \text{ cm}^2
\]
4. Add these results to find the total surface area:
\[
A = 126 + 84 + 54 = 264 \text{ cm}^2
\]
Thus, the surface area of the open-top box is \( 264 \) cm\(^2\).
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Simplify this solution Extra Insights
To find the surface area of the open-top box, we can plug in the values of length \( L = 9 \) cm, width \( W = 6 \) cm, and height \( H = 7 \) cm into the formula \( A = 2 L H + 2 W H + L W \). Calculating each term: - \( 2 L H = 2 \times 9 \times 7 = 126 \) cm² - \( 2 W H = 2 \times 6 \times 7 = 84 \) cm² - \( L W = 9 \times 6 = 54 \) cm² Now, adding them up: \[ A = 126 + 84 + 54 = 264 \text{ cm}² \] Thus, the surface area of the open-top box is \( 264 \text{ cm}² \).
