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# In the figure below, O is the center of the circle. If the area of the

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Math Expert
Joined: 02 Sep 2009
Posts: 54371
In the figure below, O is the center of the circle. If the area of the  [#permalink]

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07 Jul 2017, 00:07
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Difficulty:

15% (low)

Question Stats:

83% (01:14) correct 17% (01:16) wrong based on 62 sessions

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In the figure below, O is the center of the circle. If the area of the sector containing the angle x° is 2π, what is the value of x?

(A) 22.5
(B) 30.0
(C) 45.0
(D) 60.0
(E) 90.0

Attachment:

2017-07-07_1106.png [ 7.11 KiB | Viewed 1351 times ]

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Re: In the figure below, O is the center of the circle. If the area of the  [#permalink]

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07 Jul 2017, 00:16
Given in the problem,
Area of the sector= 2π
Also given, r= 4
so, Area of the circle= πr^2
= 16π

We know that.
Area of a given sector= sector angle/360(Area of circle)

So,
Area of sector= x/360(16π)
or, 2π = x/360(16π)
0r, x = 360x2/16 = 45 degress.

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Re: In the figure below, O is the center of the circle. If the area of the  [#permalink]

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07 Jul 2017, 01:32
Using proportions to solve this question : x/360 = 2 pi /2pi4^2 = 2pi/32pi.

Solving for x, we get x=22.5°

Regards,
Shreya

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In the figure below, O is the center of the circle. If the area of the  [#permalink]

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07 Jul 2017, 03:34
shreyashree wrote:
Using proportions to solve this question : x/360 = 2 pi /2pi4^2 = 2pi/32pi.

Solving for x, we get x=22.5°

Regards,
Shreya

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app

Highlighted part should be $$pi*4^2$$
and this will result in x = 45°
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In the figure below, O is the center of the circle. If the area of the  [#permalink]

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07 Jul 2017, 07:20
Bunuel wrote:
In the figure below, O is the center of the circle. If the area of the sector containing the angle x° is 2π, what is the value of x?

(A) 22.5
(B) 30.0
(C) 45.0
(D) 60.0
(E) 90.0

Attachment:
2017-07-07_1106.png

Given;

$$C^{\circ} = x^{\circ}$$ ------------($$C^{\circ}$$ is the Central Angle)

Area of Sector $$= 2\pi$$

Radius $$= 4$$

Area of Sector $$= \pi(r^2)\frac{C^{\circ}}{360^{\circ}}$$ ------------($$C^{\circ}$$ is the Central Angle, $$r$$ is the radius)

$$2\pi = \pi(4^2) \frac{x}{360}$$

$$x^{\circ} = \frac{2*360}{16} = 45^{\circ}$$

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Re: In the figure below, O is the center of the circle. If the area of the  [#permalink]

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08 Jul 2017, 09:27
easy C.

2*pi/16*pi = 1/8

so x = (1/8) * 360 = 45
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Re: In the figure below, O is the center of the circle. If the area of the  [#permalink]

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12 Jul 2017, 16:47
1
Bunuel wrote:
In the figure below, O is the center of the circle. If the area of the sector containing the angle x° is 2π, what is the value of x?

(A) 22.5
(B) 30.0
(C) 45.0
(D) 60.0
(E) 90.0

If a circle has area A, then the area of a sector of x degrees in the circle is x/360 * A. Since the radius is 4, the area of the circle is πr^2 = 16π.

We can create the following equation and determine x:

(x/360)(16π) = 2π

16x/360 = 2

2x/45 = 2

2x = 90

x = 45

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Re: In the figure below, O is the center of the circle. If the area of the   [#permalink] 12 Jul 2017, 16:47
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