The diameter of a solid shaft is D. The inside and outside diameters of a hollow shaft of same material and length are $\frac{D}{\sqrt{3}}$ and $\frac{2D}{\sqrt{3}}$ respectively. What is the ratio of the weight of the hollow shaft to that of the solid shaft?
(a) 1 : 1 (b) 1 :$\sqrt{3}$
(c) 1 : 2 (d) 1 : 3