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# If O is the center of the circle in the figure above and the area of I

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Math Expert
Joined: 02 Sep 2009
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If O is the center of the circle in the figure above and the area of I  [#permalink]

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19 Oct 2016, 22:41
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:06) correct 25% (00:59) wrong based on 183 sessions

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If O is the center of the circle in the figure above and the area of the unshaded sector is 5, what is the area of the shaded region?

A. 25/√π
B. 30/√π
C. 20
D. 25
E. 30

Attachment:

T6126.png [ 10.21 KiB | Viewed 3082 times ]

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Re: If O is the center of the circle in the figure above and the area of I  [#permalink]

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20 Oct 2016, 01:26
1

60 -- 5

300 -- ?

Cross multiply; $$(300*5)/60 = 25$$
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Re: If O is the center of the circle in the figure above and the area of I  [#permalink]

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20 Oct 2016, 02:45
Bunuel wrote:

If O is the center of the circle in the figure above and the area of the unshaded sector is 5, what is the area of the shaded region?

A. 25/√π
B. 30/√π
C. 20
D. 25
E. 30

Attachment:
T6126.png

60/360 = 1/6

1/6 of total area = 5

5/6 of total area = 5*5 =25

D

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If O is the center of the circle in the figure above and the area of I  [#permalink]

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20 Oct 2016, 06:45
1
Bunuel wrote:

If O is the center of the circle in the figure above and the area of the unshaded sector is 5, what is the area of the shaded region?

A. 25/√π
B. 30/√π
C. 20
D. 25
E. 30

Attachment:
T6126.png

Shaded region $$= \frac{1}{6}$$

Now, 5 $$= \frac{x}{6}$$

Or, x = 30

So, Area of Unshaded region = 30 - 5 => 25

Hence answer will definitely be (D) 25

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Re: If O is the center of the circle in the figure above and the area of I  [#permalink]

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20 Oct 2016, 08:29
Bunuel wrote:

If O is the center of the circle in the figure above and the area of the unshaded sector is 5, what is the area of the shaded region?

A. 25/√π
B. 30/√π
C. 20
D. 25
E. 30

Attachment:
T6126.png

Area of a circle = πR^2 (R = radius of a circle)

Shaded area = (360 - 60/360)th part of the circle = 300/360th or 5/6th part of a circle
Area of the circle = 25* (6/5) = 30

Area of the shaded region = 30 - 5 = 25

Correct Option: D
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Joined: 11 Jul 2016
Posts: 80
Re: If O is the center of the circle in the figure above and the area of I  [#permalink]

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22 Oct 2016, 05:31
Area of sector AOB
=> pi * R^2 (60/360)
=> Pi * R^2 = 30 ........(1)

Area of circle = Pi * R^2 = 30 (from 1)

Area of shaded region = Area of circle - Area of sector AOB
= 30 - 5 = 25

Hence D
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Re: If O is the center of the circle in the figure above and the area of I  [#permalink]

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02 Nov 2016, 18:42
If you've read the circle section of the GMATclub math book, then this will be a fairly easy question -

Area of sector = pi r^2 (C/360) --> pi r^2 (60/360) =5 --> pi r^2 (1/6) = 5 --> pi r^2 = 30

So we know the area of the entire circle is 30, so the area of the shaded region is 30-5 = 25
Intern
Joined: 11 Mar 2015
Posts: 34
Re: If O is the center of the circle in the figure above and the area of I  [#permalink]

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02 Dec 2017, 07:09
We get,
60/360*πr^2=5
=>1/6*πr^2=5
=>πr^2=30 (both side multiple by 6)
Re: If O is the center of the circle in the figure above and the area of I   [#permalink] 02 Dec 2017, 07:09
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