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

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Bunuel
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What is the area of the circle shown above with center O, if the area [#permalink] New post   12 Sep 2018, 00:30
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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. \(40\sqrt{3}\pi\)


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Re: What is the area of the circle shown above with center O, if the area [#permalink] New post   12 Sep 2018, 02:59
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Bunuel wrote:

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


Show Spoiler
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] New post   12 Sep 2018, 05:46
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Bunuel wrote:

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

Show Spoiler
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] New post   12 Sep 2018, 05:49
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GMATinsight wrote:
Bunuel wrote:

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

Show Spoiler
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

______________________
Edited the typo. Thank you.
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GynCliff
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Re: What is the area of the circle shown above with center O, if the area [#permalink] New post   26 Jan 2022, 09:32
Hello, here is my question, how do you get rsq to be \(a^2\)=\(4/\sqrt{3}\)*30?

Can you please do it step by step.

For me I get r sqd to be 120 / [square_root]3
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Re: What is the area of the circle shown above with center O, if the area [#permalink] New post   27 Jan 2022, 03:14
GynCliff wrote:
Hello, here is my question, how do you get rsq to be \(a^2\)=\(4/\sqrt{3}\)*30?

Can you please do it step by step.

For me I get r sqd to be 120 / [square_root]3


Please check the attachment.
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Re: What is the area of the circle shown above with center O, if the area [#permalink]
27 Jan 2022, 03:14
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