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

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Math Expert
Joined: 02 Sep 2009
Posts: 55271
What is the area of the circle shown above with center O, if the area  [#permalink]

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12 Sep 2018, 00:30
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Difficulty:

15% (low)

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 [ 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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12 Sep 2018, 02:59
1
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. $$40\sqrt{30}\pi$$

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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12 Sep 2018, 05:46
1
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. $$40\sqrt{30}\pi$$

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)

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Posts: 55271
Re: What is the area of the circle shown above with center O, if the area  [#permalink]

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12 Sep 2018, 05:49
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. $$40\sqrt{30}\pi$$

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)

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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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