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# What is the area of the shaded portion in circle O, as pictured above

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Math Expert
Joined: 02 Sep 2009
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What is the area of the shaded portion in circle O, as pictured above  [#permalink]

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17 Aug 2018, 11:16
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79% (02:04) correct 21% (01:52) wrong based on 44 sessions

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What is the area of the shaded portion in circle O, as pictured above, with ∠O = 60° and radius r = 10?

A) $$\frac{50}{3}\pi-50\sqrt{3}$$

B) $$\frac{50}{3} \pi − 50$$

C) $$\pi \sqrt{3}$$

D) $$\frac{50}{3} \pi-25\sqrt{3}$$

E) $$\frac{50}{3} \pi$$

Attachment:

Geometry_Q14Image.jpg [ 6.99 KiB | Viewed 495 times ]

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What is the area of the shaded portion in circle O, as pictured above  [#permalink]

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17 Aug 2018, 11:39
Bunuel wrote:

What is the area of the shaded portion in circle O, as pictured above, with ∠O = 60° and radius r = 10?

A) $$\frac{50}{3}\pi-50\sqrt{3}$$

B) $$\frac{50}{3} \pi − 50$$

C) $$\pi \sqrt{3}$$

D) $$\frac{50}{3} \pi-25\sqrt{3}$$

E) $$\frac{50}{3} \pi$$

Attachment:
Geometry_Q14Image.jpg

Required area of shaded portion= Area of sector made by the minor arc(shaded arc)- Area of triangle AOB(Let AB be the line segment)
Area of sector=$$\pi*10^2$$*$$\frac{1}{6}$$=$$\frac{50}{3}\pi$$.........(1)
Area of equilateral triangle AOB=$$\sqrt{3}/4*10^2$$=$$25\sqrt{3}$$...(2)
So,area of shaded portion=$$\frac{50}{3}\pi$$-25$$\sqrt{3}$$

Ans. (D)
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What is the area of the shaded portion in circle O, as pictured above   [#permalink] 17 Aug 2018, 11:39
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