A cuboid has a surface area of 102.
Calculate X.
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A cuboid has a surface area of 102.
Calculate X.
To solve this problem, we will use the formula for the surface area of a cuboid:
Given:
Substitute the known values into the surface area formula:
Simplify by calculating the known products:
Combine like terms:
Distribute the 2 across the terms inside the parentheses:
To isolate , subtract 42 from both sides:
Finally, divide both sides by 20 to solve for :
Therefore, the solution to the problem is .
3
A cuboid is shown below:
What is the surface area of the cuboid?
A cuboid has 6 faces that come in 3 pairs of identical rectangles. Each pair (top/bottom, front/back, left/right) has the same area, so we calculate 3 different areas and multiply by 2.
It doesn't matter! You can assign length, width, and height to any of the three dimensions. The surface area formula works regardless of which dimension you call l, w, or h.
Check your arithmetic! Dimensions must be positive numbers since they represent physical measurements. A negative result means there's an error in your calculations.
No, you need the formula! The surface area formula is the only way to relate the given surface area (102) to the unknown dimension X. Memorize it:
Both terms have the same variable X, so we can add their coefficients: 7X + 3X = 10X. This simplifies our equation and makes it easier to solve for X.
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