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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 11 Sep 2018, 23:30
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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. \(40\sqrt{3}\pi\)


Attachment:
image001.jpg
image001.jpg [ 1.99 KiB | Viewed 340 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, 01:59
1
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, 04:46
1
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, 04:49
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

______________________
Edited the typo. Thank you.
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: What is the area of the circle shown above with center O, if the area &nbs [#permalink] 12 Sep 2018, 04:49
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