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.
+130085 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
