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In the diagram, \(K ,O and M\) are the centers of three semi- circles. Also, \(OC = 32\)and  \(CB=36\).

What is the area of the shaded region.

 Dec 11, 2018
 #1
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Note that the radius of the largest circle is  OC + CB = 32 + 36 =  68

 

The radius of the smallest circle is (1/2)CB = (1/2)(36) = 18

 

The radius of the intermediate circle is the tricky one to figure !!!

 

Note that AO is the radius of the largest circle = 68

And OC = 32

 

So....AO + OC = the diameter of the intermediate circle = 68 + 32 = 100

 

So....the radius of this circle = 50

 

So....the shded area is

 

Area of largest circle - area of the other two circles =

 

pi  * [ 68^2 - (50^2 + 18^2) ]  =

 

pi  * [ 4624 - ( 2500 + 324) ]   =

 

pi * [ 4624 - 2824]  =

 

pi * [ 1800] units^2   ≈  5654.87 units^2

 

 

cool cool cool

 Dec 11, 2018

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