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505-555 Level|   Geometry|      
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Bunuel
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In the figure below, O is the center of the circle. If the area of the 07 Jul 2017, 00:07
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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82% (01:07) correct 18% (01:16) wrong based on 78 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


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Attachment:
2017-07-07_1106.png
2017-07-07_1106.png [ 7.11 KiB | Viewed 3475 times ]
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C
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In the figure below, O is the center of the circle. If the area of the 07 Jul 2017, 00:16
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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.

Hence, C is the ANSWER




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In the figure below, O is the center of the circle. If the area of the 07 Jul 2017, 01:32
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Using proportions to solve this question : x/360 = 2 pi /2pi4^2 = 2pi/32pi.

Solving for x, we get x=22.5°

Answer is option A.

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In the figure below, O is the center of the circle. If the area of the 07 Jul 2017, 03:34
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shreyashree
Using proportions to solve this question : x/360 = 2 pi /2pi4^2 = 2pi/32pi.

Solving for x, we get x=22.5°

Answer is option A.

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 07 Jul 2017, 07:20
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Bunuel
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


Show Spoiler
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)

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

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

Answer (C)...
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In the figure below, O is the center of the circle. If the area of the 08 Jul 2017, 09:27
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easy C.

2*pi/16*pi = 1/8

so x = (1/8) * 360 = 45
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In the figure below, O is the center of the circle. If the area of the 12 Jul 2017, 16:47
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Bunuel
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

Answer: C
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