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29 Aug 2018, 01:52
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
90% (01:38) correct
10%
(02:14)
wrong
based on 109
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What is area of the sector ACBO in the circle above with center O, if the radius of the circle is 6 and the length of the arc ACB is 2π?
A. \(6\pi\)
B. \(6\pi - 6\)
C. \(6\pi - 9\)
D. \(6\pi-\frac{25}{2}\)
E. \(6\pi-9\sqrt{3}\)
Attachment:
circle7168.jpg [ 26.19 KiB | Viewed 4492 times ]
29 Aug 2018, 06:39
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Bunuel
Circumference = 2π(radius)
Given: radius is 6
So, circumference = 2π(6) = 12π
We're told the arc ACB has length 2π
2π/12π = 1/6.
So, the arc represents 1/6 of the circle's entire circumference
This also means sector ACBO represents 1/6 of the circle's area
Area of circle = π(radius)²
So, area of this circle = π(6)² = 36π
So, the area of sector ACBO = 1/6 of 36π
= 6π
Answer: A
Cheers,
Brent
General Discussion
29 Aug 2018, 01:58
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Bunuel
Length of the arc = \(2 pi r @/360\) =\(2 pi\)
@=60
area of sector = \(pi r^2 @/360\) = \(pi * 36/6\) = 6 pi
