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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.

Guest Dec 11, 2018

#1**+1 **

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

CPhill Dec 11, 2018