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What is the area of the circle shown above with center O, if the area

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What is the area of the circle shown above with center O, if the area  [#permalink]

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New post 12 Sep 2018, 00:30
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C
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E

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Question Stats:

85% (01:38) correct 15% (02:53) wrong based on 25 sessions

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What is the area of the circle shown above with center O, if the area of the equilateral triangle inside the circle is 30 square units?


A. \(2\sqrt{30}\pi\)

B. \(15\sqrt{3}\pi\)

C. \(30\pi\)

D. \(60\pi\)

E. \(40\sqrt{3}\pi\)


Attachment:
image001.jpg
image001.jpg [ 1.99 KiB | Viewed 475 times ]

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Re: What is the area of the circle shown above with center O, if the area  [#permalink]

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New post 12 Sep 2018, 02:59
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Bunuel wrote:
Image
What is the area of the circle shown above with center O, if the area of the equilateral triangle inside the circle is 30 square units?


A. \(2\sqrt{30}\pi\)

B. \(15\sqrt{3}\pi\)

C. \(30\pi\)

D. \(60\pi\)

E. \(40\sqrt{30}\pi\)


Attachment:
image001.jpg



Notice that radius of the circle=side of the equilateral triangle

Given Area of equilateral triangle=30
Or, \(\sqrt{3}/4*a^2\)
Or, \(a^2\)=\(4/\sqrt{3}\)*30

Area of circle=π\(a^2\)=\(40\sqrt{3}π\)

I think there is a typographical error in option E.
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Re: What is the area of the circle shown above with center O, if the area  [#permalink]

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New post 12 Sep 2018, 05:46
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Bunuel wrote:
Image
What is the area of the circle shown above with center O, if the area of the equilateral triangle inside the circle is 30 square units?


A. \(2\sqrt{30}\pi\)

B. \(15\sqrt{3}\pi\)

C. \(30\pi\)

D. \(60\pi\)

E. \(40\sqrt{30}\pi\)

Attachment:
image001.jpg


Area of the equilateral triangle \(= (√3/4)*r^2\) where r is the radius of the circle and length of each side of equilateral triangle

i.e. \((√3/4)*r^2 = 30\)
i.e. \(r^2 = 40√3\)
i.e. Area of the circle = \(π*r^2 = 40√3π\)

Answer: Option E (After correction in the option mentioned)

Bunuel : Please modify the answer option E
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Re: What is the area of the circle shown above with center O, if the area  [#permalink]

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New post 12 Sep 2018, 05:49
GMATinsight wrote:
Bunuel wrote:
Image
What is the area of the circle shown above with center O, if the area of the equilateral triangle inside the circle is 30 square units?


A. \(2\sqrt{30}\pi\)

B. \(15\sqrt{3}\pi\)

C. \(30\pi\)

D. \(60\pi\)

E. \(40\sqrt{30}\pi\)

Attachment:
image001.jpg


Area of the equilateral triangle \(= (√3/4)*r^2\) where r is the radius of the circle and length of each side of equilateral triangle

i.e. \((√3/4)*r^2 = 30\)
i.e. \(r^2 = 40√3\)
i.e. Area of the circle = \(π*r^2 = 40√3π\)

Answer: Option E (After correction in the option mentioned)

Bunuel : Please modify the answer option E

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Edited the typo. Thank you.
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Re: What is the area of the circle shown above with center O, if the area   [#permalink] 12 Sep 2018, 05:49
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