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Geometry

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In the diagram, K, O, and M are the centers of the three semi-circles. Also, OC  = 32 and CB = 36. What is the area of the shaded region? Jun 29, 2018

#1
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diameter of circle  M  =  CB  =  36

radius of circle  M  =  36 / 2  =  18

area of semicircle  M  =  (1/2)pi( 182 )  =  162pi

radius of circle  O  =  OC + CB  =  32 + 36  =  68

diameter of circle  O  =  AB  =  2 * 68  =  136

area of semicircle  O  =  (1/2)pi( 682 )  =  2312pi

diameter of circle  K  =  AB - CB  =  136 - 36  =  100

radius of circle  K  =  100 / 2  =  50

area of semicircle  K  =  (1/2)pi( 502 )  =  1250pi

area of shaded region   =   area of semicircle O  -  area of semicircle K  -  area of semicircle M

area of shaded region   =   2312pi  -  1250pi  -  162pi

area of shaded region   =   900pi

Jun 29, 2018

#1
+2

diameter of circle  M  =  CB  =  36

radius of circle  M  =  36 / 2  =  18

area of semicircle  M  =  (1/2)pi( 182 )  =  162pi

radius of circle  O  =  OC + CB  =  32 + 36  =  68

diameter of circle  O  =  AB  =  2 * 68  =  136

area of semicircle  O  =  (1/2)pi( 682 )  =  2312pi

diameter of circle  K  =  AB - CB  =  136 - 36  =  100

radius of circle  K  =  100 / 2  =  50

area of semicircle  K  =  (1/2)pi( 502 )  =  1250pi

area of shaded region   =   area of semicircle O  -  area of semicircle K  -  area of semicircle M

area of shaded region   =   2312pi  -  1250pi  -  162pi

area of shaded region   =   900pi

hectictar Jun 29, 2018