A semi-circle of radius 4cm has the same area as a complete circle of radius r cm. What is the radius of the complete circle?

posons r radius de semi circle 

et r' radius de complete circle

on a :   ( 2*r*pi ) / 2 = 2*r'*pi

             r*pi = 2*r'*pi

             r = 2r'

      d'ou r = 4 cm =2r'

     donc r' = 4/2 = 2

alors r' = 2

Area of semicircle: A1 = (1/2)*pi*4^2

 

Area of complete circle: A2 = pi*r^2

 

If A1 = A2 then pi *r^2 = (1/2)*pi*4^2

 

r^2 = (1/2)*16

 

r^2 = 8

 

r = sqrt(8)  or r = 2*sqrt(2) cm

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