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What is area of the sector ACBO in the circle above with center O, if

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What is area of the sector ACBO in the circle above with center O, if  [#permalink]

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New post 29 Aug 2018, 01:52
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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
circle7168.jpg [ 26.19 KiB | Viewed 896 times ]

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Re: What is area of the sector ACBO in the circle above with center O, if  [#permalink]

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New post 29 Aug 2018, 01:58
Bunuel wrote:
Image
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



Length of the arc = \(2 pi r @/360\) =\(2 pi\)
@=60
area of sector = \(pi r^2 @/360\) = \(pi * 36/6\) = 6 pi
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Re: What is area of the sector ACBO in the circle above with center O, if  [#permalink]

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New post 29 Aug 2018, 06:39
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Bunuel wrote:
Image
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


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
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Re: What is area of the sector ACBO in the circle above with center O, if  [#permalink]

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New post 29 Aug 2018, 08:52
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Bunuel wrote:
Image
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:
1535558073928.jpg
1535558073928.jpg [ 51.45 KiB | Viewed 721 times ]
Answer is A
Attachment:
1535558073928.jpg
1535558073928.jpg [ 51.45 KiB | Viewed 721 times ]


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Re: What is area of the sector ACBO in the circle above with center O, if  [#permalink]

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New post 29 Aug 2018, 10:46
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\(A = \frac{S}{2πR} * πR^2\)

S = Arc Length = 2π

R = radius = 6

\(A = \frac{2π}{2π6} * 6^2\) = \(\frac{2π}{12π} * 36\) = \(6π\)

:-)
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Area of a sector of a circle.png
Area of a sector of a circle.png [ 268.11 KiB | Viewed 686 times ]

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Re: What is area of the sector ACBO in the circle above with center O, if  [#permalink]

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New post 03 Sep 2018, 15:06
Just need to remember 2 formulas to solve this,

1) Find @(Theta) using below formula.

Circumference of Arc =@/360 * 2 PIE R

2) Add value of in below equation.

Area of Sector = @/360 * PIE Rsquare
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Re: What is area of the sector ACBO in the circle above with center O, if   [#permalink] 03 Sep 2018, 15:06
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