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In the figure above, the circle O has a radius of 6. What is the area

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In the figure above, the circle O has a radius of 6. What is the area  [#permalink]

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New post 20 Feb 2018, 23:49
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In the figure above, the circle O has a radius of 6. What is the area of the shaded portion of the figure?


A. \(\frac{\pi}{2}\)

B. \(\frac{5\pi}{2}\)

C. \(12\pi\)

D. \(18\pi\)

E. \(30\pi\)


Attachment:
2018-02-21_1019_002.png
2018-02-21_1019_002.png [ 17.61 KiB | Viewed 662 times ]

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Re: In the figure above, the circle O has a radius of 6. What is the area  [#permalink]

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New post 21 Feb 2018, 00:58
Let the angle formed by quadrilateral at point O= x

\(x^{\circ}\)+\(110^{\circ}\)+\(70^{\circ}\)+\(120^{\circ}\)= \(360^{\circ}\)

x+300= 360; x= 360-300= \(60^{\circ}\)

Angle formed by point O in the shaded region= 360-x= 360-60= \(300^{\circ}\)

Area of shaded region= \(\frac{300}{360}\)*\(\pi\)*\((6)^2\)= 30\(\pi\)

Answer: E.
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Re: In the figure above, the circle O has a radius of 6. What is the area  [#permalink]

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New post 21 Feb 2018, 03:04
Bunuel wrote:
Image
In the figure above, the circle O has a radius of 6. What is the area of the shaded portion of the figure?


A. \(\frac{\pi}{2}\)

B. \(\frac{5\pi}{2}\)

C. \(12\pi\)

D. \(18\pi\)

E. \(30\pi\)


Attachment:
2018-02-21_1019_002.png


area of sector = #/360 x pi r^2 ( # is angle of sector at centre)

#= 360 - 300 = 60 ( as per diagram) = 1/6 pi r^2 = 36/6 = 6 pi

Area of sector = 6 pi

Area of cirlce = pi x 6 x6 = 36 pi

Shaded area = 36-6 pi = 30 pi

(E)
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Re: In the figure above, the circle O has a radius of 6. What is the area  [#permalink]

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New post 21 Feb 2018, 23:02
Bunuel wrote:
Image
In the figure above, the circle O has a radius of 6. What is the area of the shaded portion of the figure?


A. \(\frac{\pi}{2}\)

B. \(\frac{5\pi}{2}\)

C. \(12\pi\)

D. \(18\pi\)

E. \(30\pi\)
Straight IMO is E as above quadrilateral 4th side is 360-(110+120+70)=60 and rest of the angle is 360-60=300. so area of shaded region is 300*pie*6^2/360= 30pie which is option E
*Inner angle of circle is 360 and sum of all the angles in quadrilateral is also 360.

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2018-02-21_1019_002.png
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Re: In the figure above, the circle O has a radius of 6. What is the area &nbs [#permalink] 21 Feb 2018, 23:02
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In the figure above, the circle O has a radius of 6. What is the area

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