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

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

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29 Aug 2018, 00:52
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Difficulty:

15% (low)

Question Stats:

92% (01:29) correct 8% (02:13) wrong based on 39 sessions

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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 561 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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29 Aug 2018, 00:58
Bunuel wrote:

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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29 Aug 2018, 05:39
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Bunuel wrote:

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

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

So, area of this circle = π(6)² = 36π

So, the area of sector ACBO = 1/6 of 36π
= 6π

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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29 Aug 2018, 07:52
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Bunuel wrote:

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 [ 51.45 KiB | Viewed 404 times ]
Attachment:

1535558073928.jpg [ 51.45 KiB | Viewed 404 times ]

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Joined: 09 Mar 2016
Posts: 1110
Re: What is area of the sector ACBO in the circle above with center O, if  [#permalink]

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29 Aug 2018, 09:46
2
$$A = \frac{S}{2πR} * πR^2$$

S = Arc Length = 2π

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

Attachments

Area of a sector of a circle.png [ 268.11 KiB | Viewed 369 times ]

Intern
Joined: 21 Jul 2018
Posts: 40
Re: What is area of the sector ACBO in the circle above with center O, if  [#permalink]

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03 Sep 2018, 14:06
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 &nbs [#permalink] 03 Sep 2018, 14:06
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