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Updated on: 19 Feb 2020, 01:17
Originally posted by QuantMadeEasy on 19 Feb 2020, 01:06.
Last edited by Bunuel on 19 Feb 2020, 01:17, edited 1 time in total.
Last edited by Bunuel on 19 Feb 2020, 01:17, edited 1 time in total.
Renamed the topic and edited the question.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
67% (01:26) correct
33%
(01:35)
wrong
based on 46
sessions
History
Date
Time
Result
Not Attempted Yet
What is the area of the shaded region?
(1) The ratio of length of arc ABC to circumference of the circle is 1:6
(2) The area of triangle AOC is 9√3
Attachment:
Untitled.png [ 9.08 KiB | Viewed 2256 times ]
19 Feb 2020, 01:58
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First you use (a)
you can calculate the area of the Circle and dived by 6 to get the triangle with the red area
1/6*pi*r^2
Then use the triangle from (b)
you can calculate the angle in the middle as 360/6=60 thus all sides are equal.
and then you can calculate easily the sides, get the radius and lastly calculate the actual Area of the circle from which you subtract the triangle area and you have the answer.
I don't think it is needed to calculate numbers because it takes time, just having a correct thought process that fits is enought to asnwer the question.
Answer C
you can calculate the area of the Circle and dived by 6 to get the triangle with the red area
1/6*pi*r^2
Then use the triangle from (b)
you can calculate the angle in the middle as 360/6=60 thus all sides are equal.
and then you can calculate easily the sides, get the radius and lastly calculate the actual Area of the circle from which you subtract the triangle area and you have the answer.
I don't think it is needed to calculate numbers because it takes time, just having a correct thought process that fits is enought to asnwer the question.
Answer C
Updated on: 21 Feb 2020, 22:38
Originally posted by QuantMadeEasy on 19 Feb 2020, 02:47.
Last edited by QuantMadeEasy on 21 Feb 2020, 22:38, edited 1 time in total.
Last edited by QuantMadeEasy on 21 Feb 2020, 22:38, edited 1 time in total.
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Q. What is the area of the shaded region ?
Analyzing the question stem
Area of shaded region = area of the sector – area of the triangle
We know to calculate area of the sector, central angle and radius are required.
Analysing the statement
1) The ratio of length of arc ABC to circumference of the circle is 1:6
Ratio of length of arc to cicumference of the circle = ratio of cental angle to complete angle = 1:6.
Central angle = 1/6 * 360 = 60
Deriving further
AO = CO = radius and angle AOC = 60. Therefore triangle AOC is equilateral.
As radius is unknown, area of the shaded region cannot be calculated.
Insufficient
2) The area of triangle AOC is 9√3
Area of the sector is unknown.
Insufficient
Combining statement (1) and (2)
area of equilateral traingle = \(\frac{√3}{4}\) \(a^2\) = 9√3
From this, radius will be calculated and hence sector area.
Sufficient
C is correct
Analyzing the question stem
Area of shaded region = area of the sector – area of the triangle
We know to calculate area of the sector, central angle and radius are required.
Analysing the statement
1) The ratio of length of arc ABC to circumference of the circle is 1:6
Ratio of length of arc to cicumference of the circle = ratio of cental angle to complete angle = 1:6.
Central angle = 1/6 * 360 = 60
Deriving further
AO = CO = radius and angle AOC = 60. Therefore triangle AOC is equilateral.
As radius is unknown, area of the shaded region cannot be calculated.
Insufficient
2) The area of triangle AOC is 9√3
Area of the sector is unknown.
Insufficient
Combining statement (1) and (2)
area of equilateral traingle = \(\frac{√3}{4}\) \(a^2\) = 9√3
From this, radius will be calculated and hence sector area.
Sufficient
C is correct
