In the figure, the visible gray area within the larger circle is equal to eight 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.
Since we can position the white circle anywhere in the gray area, let the circles be concentric
Area of larger circle = pi*r^2 + 8pir^2 = 9pi r^2 where r is the radius of the smaller circle
Ratio of areas =
_______ = 1/9
9 pi r^2
The ratio of the radii = sqrt (1/9) = 1 / 3