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In the diagram above, all the points are on a line, and the number of

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In the diagram above, all the points are on a line, and the number of [#permalink]

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In the diagram above, all the points are on a line, and the number of each point indicates how many units that point is from zero. The points #1 – #6 are the centers of the six circles, and all circles pass through point zero. What is the total area of the shaded region?

A. \(12\pi\)
B. \(21\pi\)
C. \(24\pi\)
D. \(46\pi\)
E. \(48\pi\)

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: In the diagram above, all the points are on a line, and the number of [#permalink]

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New post 11 Mar 2015, 06:47
Hi

Interesting and fun question

Moreover geometry is always fun
Plz find the attachment for the answer
Attachments

circle.png
circle.png [ 57.56 KiB | Viewed 1533 times ]


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Re: In the diagram above, all the points are on a line, and the number of [#permalink]

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New post 12 Mar 2015, 17:08
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Bunuel wrote:
Attachment:
cpotg_img6.png
In the diagram above, all the points are on a line, and the number of each point indicates how many units that point is from zero. The points #1 – #6 are the centers of the six circles, and all circles pass through point zero. What is the total area of the shaded region?

A. \(12\pi\)
B. \(21\pi\)
C. \(24\pi\)
D. \(46\pi\)
E. \(48\pi\)

Kudos for a correct solution.


Shaded region 1: 4pi-pi=3 pi
Shaded region 2: 16pi-9pi = 7pi
Shaded region 3: 36pi-25pi=11pi

Total = 21 pi which is answer B.
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Re: In the diagram above, all the points are on a line, and the number of [#permalink]

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Answer = B. \(21\pi\)

Radii of all green shaded circles is even i.e 2, 4, 6

Radii of all white circles is odd i.e 1, 3, 5

Area of required shaded region \(= \pi(2^2 + 4^2 + 6^2) - \pi(1^2 + 3^2 + 5^2)\)

\(= \pi(4+16+36 - 1 - 9 - 25) = 21\pi\)
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Re: In the diagram above, all the points are on a line, and the number of [#permalink]

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New post 15 Mar 2015, 21:36
Bunuel wrote:
Image
In the diagram above, all the points are on a line, and the number of each point indicates how many units that point is from zero. The points #1 – #6 are the centers of the six circles, and all circles pass through point zero. What is the total area of the shaded region?

A. \(12\pi\)
B. \(21\pi\)
C. \(24\pi\)
D. \(46\pi\)
E. \(48\pi\)

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

First, let’s look at the outer “lobe,” the one between 10 and 12. The circle through point 12 has a center a 6 and radius of 6, so its area is 36pi. The circle through point 10 has a center a 5 and radius of 5, so its area is 25pi. If we subtract the latter from the former, we an area of 11pi for this lobe.

Now, let’s look the middle lobe, the one between 6 and 8. The circle through point 6 has a center a 3 and radius of 3, so its area is 9pi. The circle through point 8 has a center a 4 and radius of 4, so its area is 16pi. If we subtract the latter from the former, we an area of 7pi for this lobe.

Now, let’s look the smallest lobe, the one between 2 and 4. The circle through point 2 has a center a 1 and radius of 1, so its area is pi. The circle through point 4 has a center a 2 and radius of 2, so its area is 4pi. If we subtract the latter from the former, we an area of 3pi for this lobe.

Add the areas of the three separate lobes: 3pi +7pi + 11pi = 21pi.

Answer = (B)
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Re: In the diagram above, all the points are on a line, and the number of [#permalink]

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New post 08 Jul 2016, 01:54
We divide the it into 3 parts with 2 circles each then add the 3 parts to get the total area as follows:
[pi(2)^2-pi(1)^2] + [pi(4)^2-pi(3)^2]+[pi(6)^2-pi(5)^2]
=3pi + 7pi + 11pi
=21 pi
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Re: In the diagram above, all the points are on a line, and the number of [#permalink]

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New post 08 Jul 2016, 05:30
Bunuel wrote:
Attachment:
cpotg_img6.png
In the diagram above, all the points are on a line, and the number of each point indicates how many units that point is from zero. The points #1 – #6 are the centers of the six circles, and all circles pass through point zero. What is the total area of the shaded region?

A. \(12\pi\)
B. \(21\pi\)
C. \(24\pi\)
D. \(46\pi\)
E. \(48\pi\)

Kudos for a correct solution.


36pi-25pi+16pi-9pi+4pi-pi

we are subtracting (25+9+1) i.e. an odd number from even number. Answer will be odd and there is only only odd option in the answer choices.

B is the answer
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Re: In the diagram above, all the points are on a line, and the number of [#permalink]

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Re: In the diagram above, all the points are on a line, and the number of   [#permalink] 08 Sep 2017, 09:31
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