+77 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?
+9479 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
+9479 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
