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The area of the circular region

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The area of the circular region [#permalink] New post 14 Dec 2016, 02:10
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The area of the circular region with center P is 16pi

Quantity A
Quantity B
X
4



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The area of the circular region [#permalink] New post 29 Dec 2016, 14:56
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Carcass wrote:
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The area of the circular region with center P is 16pi

Quantity A
Quantity B
X
4




The area of the circular region with center P is 16pi
Area of circle = (pi)(r²), where r = radius of circle

So, we can write: (pi)(r²) = 16pi
Divide both sides by pi to get: r² = 16
Solve to get: r = 4

If the radius = 4, then the DIAMETER of the circle = 8
Image

Since we have a right triangle, we can apply the Pythagorean Theorem and write: x² + x² = 8²
Simplify: 2x² = 64
x² = 32
x = √32

So, we have:
Quantity A: √32
Quantity B: 4

IMPORTANT: We need not evaluate √32.
Just recognize that √16 = 4, which means √32 is greater than 4
Answer: A
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Re: The area of the circular region   [#permalink] 29 Dec 2016, 14:56
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The area of the circular region

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