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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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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 [ 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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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$$\pi$$

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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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21 Feb 2018, 03:04
Bunuel wrote:

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

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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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21 Feb 2018, 23:02
Bunuel wrote:

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.

Attachment:
2018-02-21_1019_002.png
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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