In the figure, the visible gray area within the larger circle is equal to \(8\) times the area of the white circular region. What is the ratio of the radius of the small circle to the radius of the large circle? Express your answer as a common fraction.

Guest Jan 10, 2022

#1**0 **

x = white area

larger circle area = 8x + x = 9 x

small circle area = pi r_{1}^{2 }= x

Larger circle = pi r_{2}^{2 }= 9x = 9 pi r_{1} ^{2}

pi r_{1}^{2} / 9 pi r_{1}^{2} = 1/ 9

Guest Jan 10, 2022