Flashcard 9 - Next Generation Advanced Algebra and Functions Flashcard Set for the ACCUPLACER Test

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The correct answer is:

rectangle:
perimeter = \(2l + 2w\)
area = \(lw\), where l is length and w is width

trapezoid:
perimeter = add all sides
area = \(\frac{1}{2}h(b_1 + b_2)\), where h is height, and \(b_1\) and \(b_2\) are the two bases

circle:
circumference = \(2\pi r\)
area = \(\pi r^2\), where r is radius

cylinder:
surface area = \(2\pi r^2 + 2\pi r h\)
volume = \(\pi r^2 h\), where h is height and r is radius

sphere:
surface area = \(4\pi r^2\)
volume = \(\frac{4}{3}\pi r^3\), where r is radius


Explanation:

It is useful to memorize these formulas, but more valuable to develop the ability to derive them using various methods.
Also, when using any formula, it is important to match the items in the formula with the numbers given in the problem, exactly. For example, you might be given the diameter of a circle and need to use \(\pi r^2\) to find the area. It would be necessary to divide the diameter by 2 before inserting it into the formula because the diameter is twice the radius and the radius is what you need in the formula. Read problems carefully!

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