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Each of the small circles in a figure has 1cm radio. The center circle is tangent to each of the six surrounding it, these being tangent to the big circle and its nearest neighbors. What is the area in cm^2 of the shaded area?

 

A)\( \pi\)   B)1.5\(\pi\)  C)\(\tau\)  D)3\(\pi\)  E)3.5\(\pi\)                  

 

 

 

The picture of the Circle

buubleman  Nov 30, 2015

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 #7
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Thanks, buubleman.......I always thought that "tau" was just a variable.....I didn't realize it was associated with a numerical value.......you taught ME something, too!!!

 

 

cool cool cool

CPhill  Nov 30, 2015
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 #1
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I cannot see the picture! =(

-Hay

Guest Nov 30, 2015
 #2
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  Is this clearer?

buubleman  Nov 30, 2015
 #3
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I wonder if it is blocked for me. Because all i see is blank XD.

What did it look like? if you could describe it.

-Hay

Guest Nov 30, 2015
 #4
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It's proably blocked for you as i can clearly see it. i don't really know how to describe it!

buubleman  Nov 30, 2015
 #5
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+10

 

Let us imagine that the big circle is completletly shaded and no smaller circles exist......the area of this circle  = pi(3cm)^2   = 9pi cm^2

 

And the area of the 7 smaller congruent circles is  7*pi (1 cm)^2   =  7pi cm^2

 

And these are tangent to each other and to the larger circle

 

Then, the area of the shaded part left  after the 7 smaller circles are inserted nto the larger circle  =

 

pi ( [3cm]^2  - 7 [ 1cm]^2 ] =

 

pi [ 9 cm^2 - 7cm^2]  =

 

2pi cm^2    ......this doesn't match any of the given answers......!!!!

 

[I tried to insert a picture of this but our image uploader isn't working]

 

Here's a pic of what you describe using Desmos.......https://www.desmos.com/calculator/cwrndrdb0x

 

 

cool cool cool

CPhill  Nov 30, 2015
 #6
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+5

2pi = Tau so it does match one answear. Thanks got stuck on this problem for quite a bit of time.

buubleman  Nov 30, 2015
 #7
avatar+78750 
+10
Best Answer

Thanks, buubleman.......I always thought that "tau" was just a variable.....I didn't realize it was associated with a numerical value.......you taught ME something, too!!!

 

 

cool cool cool

CPhill  Nov 30, 2015
 #8
avatar+284 
+5

Welcome! smiley

buubleman  Nov 30, 2015
 #9
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Which bit is shaded?  It is too blury for me to tell.

Obvioulsy Chris understood://

I suppose it is all the area NOT inside the little circles?

Melody  Dec 1, 2015
edited by Melody  Dec 1, 2015
 #10
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Melody....the shaded bit is the area inside the large circle that is not occupied by the seven smaller circles........I had a good GeoGebra presentation of it.....but......I can't upload any pics.....{BOO !!!]

 

 

cool cool cool

CPhill  Dec 1, 2015
edited by CPhill  Dec 1, 2015

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