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The circle shown has an area of 497r and is divided into fou

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The circle shown has an area of 497r and is divided into fou [#permalink] New post 26 Nov 2019, 17:16
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The circle shown has an area of \(49\pi\) and is divided into four sectors, all of which have a central angle of the same measure. What is the perimeter of the shaded region?

A. \(14+\frac{7\pi}{16}\)

B. \(14+\frac{7\pi}{8}\)

C. \(14+\frac{7\pi}{4}\)

D. \(14+\frac{7\pi}{2}\)

E. \(14+7\pi\)



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Re: The circle shown has an area of 497r and is divided into fou [#permalink] New post 26 Nov 2019, 18:14
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To answer this question, we need the length of the two radii, along with the length of the arc around the shaded area.

We know that since the Area of the circle is 49pi, the radii of the circle must be 7 (Area of Circle = πr^2, so 7^2*π = 49π).

Given that each radii is 7, you now have the length of the two edges of the shaded area coming from the center of the circle. 7+7 = 14.

To find the length of the arc, you first need to find the circumference of the circle. Circumference of circle = 2πr. Well, we know that r=7, so 2*7*π = 14π = Circumference. Since the stem states that the circle is divided into four sectors, we can take 1/4th of that to find the length of the arc around the shaded area. 1/4 (14) = 14π/4 = 7π/2

Add these together and you have 14 + (7π/2) -- Ans. is D.
Re: The circle shown has an area of 497r and is divided into fou   [#permalink] 26 Nov 2019, 18:14
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The circle shown has an area of 497r and is divided into fou

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