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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