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# What is the area of the shaded region if the center of the larger circ

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Math Expert
Joined: 02 Sep 2009
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What is the area of the shaded region if the center of the larger circ  [#permalink]

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29 Aug 2018, 02:26
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Difficulty:

25% (medium)

Question Stats:

73% (00:37) correct 27% (01:04) wrong based on 53 sessions

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What is the area of the shaded region if the center of the larger circle lies on the small circle, as shown?

(1) The diameter of the smaller circle is 5.
(2) The circumference of the larger circle is 10 π.

Attachment:

image003.gif [ 834 Bytes | Viewed 704 times ]

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Re: What is the area of the shaded region if the center of the larger circ  [#permalink]

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29 Aug 2018, 02:36
From 1:

Diameter of the smaller circle becomes the radius of the larger circle.

We can determine the area of the shaded region.
Area of larger circle-Area of smaller circle.
Sufficient.

From 2:

Circumference = 2*pi*r = 10Pi.
r = 5 of bigger circle.
Which is the diameter of the smaller circle.
Sufficient.

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Re: What is the area of the shaded region if the center of the larger circ  [#permalink]

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29 Aug 2018, 03:04
Bunuel wrote:

What is the area of the shaded region if the center of the larger circle lies on the small circle, as shown?

(1) The diameter of the smaller circle is 5.
(2) The circumference of the larger circle is 10 π.

Attachment:
image003.gif
To know the shaded area, we need to know the radius of any one circle.

Both statements give that info individually.

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Re: What is the area of the shaded region if the center of the larger circ  [#permalink]

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29 Aug 2018, 03:39
1. Radius of smaller circle = 2.5
Radius of larger circle = 5

Area of shaded region = Area of larger circle - Area of smaller circle

2. 2* pie * radius = 10 pie
Radius of larger circle = 5
Radius of smaller circle = 2.5

Area of shaded region = Area of larger circle - Area of smaller circle

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Re: What is the area of the shaded region if the center of the larger circ  [#permalink]

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29 Aug 2018, 05:52
Bunuel wrote:

What is the area of the shaded region if the center of the larger circle lies on the small circle, as shown?

(1) The diameter of the smaller circle is 5.
(2) The circumference of the larger circle is 10 π.

Attachment:
image003.gif

Area of shaded region = area of big circle - area of small circle

The diameter of the small circle is half that of the bigger one.

(1) Diameter of small circle is 5 > area of both circles can be calculated [SUFFICIENT]

(2) Circumference of the larger circle is is 10 π > Radii of both circles can be calculated and then areas too [SUFFICIENT]

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What is the area of the shaded region if the center of the larger circ  [#permalink]

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30 Aug 2018, 01:19
Hi @bunuel,trust you are fine. Could you please help me clarify when exactly to trust the diagram on a DS question. In this particular question, I only assumed that the centre of the larger circle lies on the smaller circles in the figure and I deduced 2 different scenarios.
1st, where the figure is as in the given question and 2nd, One where the other end of the smaller circle doesn't not touch the arc of the larger circle. Pls help me, I'm quite confused here.

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Re: What is the area of the shaded region if the center of the larger circ  [#permalink]

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30 Aug 2018, 02:09
1
Kem12 wrote:
Hi @bunuel,trust you are fine. Could you please help me clarify when exactly to trust the diagram on a DS question. In this particular question, I only assumed that the centre of the larger circle lies on the smaller circles in the figure and I deduced 2 different scenarios.
1st, where the figure is as in the given question and 2nd, One where the other end of the smaller circle doesn't not touch the arc of the larger circle. Pls help me, I'm quite confused here.

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Hi Kem12

The question specifically states 'as shown'. I hope that answers your question.
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Re: What is the area of the shaded region if the center of the larger circ  [#permalink]

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31 Aug 2018, 02:05
HinaTabassum wrote:
Kem12 wrote:
Hi @bunuel,trust you are fine. Could you please help me clarify when exactly to trust the diagram on a DS question. In this particular question, I only assumed that the centre of the larger circle lies on the smaller circles in the figure and I deduced 2 different scenarios.
1st, where the figure is as in the given question and 2nd, One where the other end of the smaller circle doesn't not touch the arc of the larger circle. Pls help me, I'm quite confused here.

Posted from my mobile device

Hi Kem12

The question specifically states 'as shown'. I hope that answers your question.

Thanks so much. this makes it clear.
Re: What is the area of the shaded region if the center of the larger circ   [#permalink] 31 Aug 2018, 02:05
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