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# Each of the triangles is equilateral.

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Director
Joined: 07 Jan 2018
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Each of the triangles is equilateral. [#permalink]  16 Aug 2018, 09:19
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Question Stats:

33% (00:47) correct 66% (01:29) wrong based on 24 sessions
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Each of the triangles is equilateral.

 Quantity A Quantity B The area of theshaded region $$6\pi$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA
Director
Joined: 20 Apr 2016
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WE: Engineering (Energy and Utilities)
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Re: Each of the triangles is equilateral. [#permalink]  17 Aug 2018, 00:11
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amorphous wrote:
Each of the triangles is equilateral.

 Quantity A Quantity B The area of theshaded region 6π

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Given the radius of the circle is 3 (since one side of the equilateral triangle is 3)

Now the area of the circle =$$\pi * radius^2 = \pi * 3^2 = 9\pi$$

Now we need to find the area of the sector covered by the 2 equilateral triangle,

$$\frac{{Sector Area}}{{circle area}} = \frac{{Central angle}}{360}$$

Sector area =$$\frac{60}{360} * circle area =\frac{60}{360} * 9\pi = \frac{{3\pi}}{2}$$

Since there are two sectors so the total sectors not covered in shaded area =$$\frac{{6\pi}}{2}$$

Therefore the area under the shaded area = circle area - area of the 2 sectors = $$9\pi - \frac{{6\pi}}{2}= \frac{{12\pi}}{2} = 6\pi$$

Hence both are equal, i.e. option C
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Director
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Re: Each of the triangles is equilateral. [#permalink]  18 Nov 2018, 15:52
pranab01 wrote:
amorphous wrote:
Each of the triangles is equilateral.

 Quantity A Quantity B The area of theshaded region 6π

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Given the radius of the circle is 3 (since one side of the equilateral triangle is 3)

Now the area of the circle =$$\pi * radius^2 = \pi * 3^2 = 9\pi$$

Now we need to find the area of the sector covered by the 2 equilateral triangle,

$$\frac{{Sector Area}}{{circle area}} = \frac{{Central angle}}{360}$$

Sector area =$$\frac{60}{360} * circle area =\frac{60}{360} * 9\pi = \frac{{3\pi}}{2}$$

Since there are two sectors so the total sectors not covered in shaded area =$$\frac{{6\pi}}{2}$$

Therefore the area under the shaded area = circle area - area of the 2 sectors = $$9\pi - \frac{{6\pi}}{2}= \frac{{12\pi}}{2} = 6\pi$$

Hence both are equal, i.e. option C

Sometime, in circle question, I have one problem. In this question, it doesn't say 'O' is the center. How would you confirm that answer is not D and calculate by confirming that 'O' is the center of the circle.
Re: Each of the triangles is equilateral.   [#permalink] 18 Nov 2018, 15:52
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