Ratio of radii of discs

The weight of a circular disc varies as the square of its radius when the thickness remains the same; it also varies as the thickness when the radius remains the same. Two discs have their thicknesses in the ratio $9:8$; find the ratio of their radii if the weight of the first is twice that of the second.

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. III. Variation, Examples III, No. 17