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Each of the triangles is equilateral.
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16 Aug 2018, 09:19
16 Aug 2018, 09:19
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Question Stats:
41% (00:51) correct
58% (01:27) wrong based on 31 sessions
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Each of the triangles is equilateral.
Quantity A |
Quantity B |
The area of the shaded 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.
Re: Each of the triangles is equilateral.
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17 Aug 2018, 00:11
17 Aug 2018, 00:11
1
amorphous wrote:
Each of the triangles is equilateral.
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.
Quantity A |
Quantity B |
The area of the shaded 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
Re: Each of the triangles is equilateral.
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18 Nov 2018, 15:52
18 Nov 2018, 15:52
pranab01 wrote:
amorphous wrote:
Each of the triangles is equilateral.
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.
Quantity A |
Quantity B |
The area of the shaded 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.
