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Calculate Surface Area of Open-Top Box with Given Length, Width, Height
Mathematics
Grade 8 (Junior High School)
Question Content
The surface area of an open-top box with length $L$, width $W$, and height $H$ can be found with the formula: $A = 2LH + 2WH + LW$. Find the surface area of an open-top box with length 8 cm, width 10 cm, and height 3 cm.
Correct Answer
188 cm²
Detailed Solution Steps
1
Step 1: Identify the given values from the problem: $L=8$ cm, $W=10$ cm, $H=3$ cm
2
Step 2: Substitute the values into the open-top box surface area formula $A = 2LH + 2WH + LW$
3
Step 3: Calculate each term separately: $2LH = 2*8*3 = 48$; $2WH = 2*10*3 = 60$; $LW = 8*10 = 80$
4
Step 4: Add the calculated terms together: $A = 48 + 60 + 80 = 188$
Knowledge Points Involved
1
Surface Area of Open-Top Rectangular Prism
The formula $A = 2LH + 2WH + LW$ calculates the total outer area of a rectangular box without a top. It sums the area of the four vertical side faces ($2LH + 2WH$) and the single bottom face ($LW$). This is used for real-world problems involving containers, storage boxes, and other open-top rectangular structures.
2
Substitution of Variables
This is the process of replacing variables in a formula with their given numerical values. It is a foundational algebra skill used to solve for unknown quantities in formulas and equations, applicable across all areas of math and science.
3
Order of Operations
When evaluating expressions, multiplication is performed before addition (following PEMDAS/BODMAS rules). This ensures consistent and correct calculation results when solving multi-step arithmetic problems.
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