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

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

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New post 17 Aug 2018, 11:16
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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:
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What is the area of the shaded portion in circle O, as pictured above  [#permalink]

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New post 17 Aug 2018, 11:39
Bunuel wrote:
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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


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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