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27 Dec 2015, 10:56
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
78% (01:08) correct
23%
(01:24)
wrong
based on 120
sessions
History
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Time
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Not Attempted Yet
What is the area of the circle above with center O?
(1) The area of ∆ AOC is 18.
(2) The length of arc ABC is 3π.
Attachment:
2015-12-27_2155.png [ 14.47 KiB | Viewed 4546 times ]
29 Dec 2015, 16:42
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Asked to find the area of circle with center O.
Area of Circle = \(\pi R^2\). So the question reduces to what is R.
Statement 1:
Area of \(\triangle AOC = 18\).
\(\frac{1}{2}\) x AO x OC = 18 (\(\triangle AOC\) is right angled at O).
AO = OC = Radius. Substituting values in above equation:
\(\frac{1}{2} R^2\) = 18. We can calculate R and hence the area of the circle.
Statement A - Sufficient.
Statement 2:
Length of the arc ABC is 3\(\pi\)
\(\frac{90}{360} 2\pi R = 3\pi\)
We can calculate the value of R from the equation above and hence area of circle.
Statement B - Sufficient as well.
Hence both the statements are sufficient. Answer D
Area of Circle = \(\pi R^2\). So the question reduces to what is R.
Statement 1:
Area of \(\triangle AOC = 18\).
\(\frac{1}{2}\) x AO x OC = 18 (\(\triangle AOC\) is right angled at O).
AO = OC = Radius. Substituting values in above equation:
\(\frac{1}{2} R^2\) = 18. We can calculate R and hence the area of the circle.
Statement A - Sufficient.
Statement 2:
Length of the arc ABC is 3\(\pi\)
\(\frac{90}{360} 2\pi R = 3\pi\)
We can calculate the value of R from the equation above and hence area of circle.
Statement B - Sufficient as well.
Hence both the statements are sufficient. Answer D
29 Dec 2015, 19:22
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Area of triangle is 18
1/2 x base x height = 36
x^2= 36
x = 6 = r
area = 36π
statement 2
arc of 90 degree is 3π
circumference is 4 x 3π = 12π
12n = 2πr
6 = r
36π
Both independantly sufficient
1/2 x base x height = 36
x^2= 36
x = 6 = r
area = 36π
statement 2
arc of 90 degree is 3π
circumference is 4 x 3π = 12π
12n = 2πr
6 = r
36π
Both independantly sufficient
