Look at the cuboid of the figure.
Its surface area is 122 cm².
What is the width of the cuboid?
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Look at the cuboid of the figure.
Its surface area is 122 cm².
What is the width of the cuboid?
To solve the problem, let's recall the formula for calculating the surface area of a cube:
(width*length + height*width + height*length) *2
Let's substitute the known values into the formula, labelling the missing side X:
2*(3*7+7*X+3*X) = 122
2*(21+7x+3x) = 122
2(21+10x) = 122
Let's now expand the parentheses:
42+20x=122
Now we move terms:
20x=122-42
20x=80
Finally, simplify:
x=4
And that's the solution!
4 cm
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 contributes the same area twice, so we calculate lw + lh + wh (one of each type) then multiply by 2!
Look carefully at the labels! In this problem, we can see dimensions 3 cm and 7 cm are given, so the unlabeled dimension is what we need to find.
Check your algebra! Dimensions must be positive since they represent real measurements. A negative result means there's an error in your calculation.
While possible, it's inefficient! Using algebraic methods with the surface area formula is faster and more reliable than trial and error.
Distribute the 2 to both terms inside: 2(21) + 2(10x) = 42 + 20x. Don't forget to multiply 2 by every term in the parentheses!
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