The ratio of weights of two spheres of different materials is 8 : 17 and the ratio of weights per 1 cc of materials of each is 289 : 64. The ratio of radii of the two spheres is

Answer: Option A

Ratio of volume of sphere × ratio of weight per 1 cc of material of each = Ratio of weight of two sphere
$$\begin{array}{rl}& \frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r_2^3}\times \frac{289}{64}=\frac{8}{17}\\ & \frac{r_1^3}{r_2^3}=\frac{8\times 64}{17\times 289}\\ & \frac{r_1}{r_2}=\frac{8\times 8\times 8}{17\times 17\times 17}\\ & \frac{r_1}{r_2}=\frac{8}{17}\\ & r_1:r_2=8:17\end{array}$$