Ratio of the volumes of two cones is 4:25 and their heights are in the ratio 25:64, then the ratio of…

The volume of a cone is $V = \frac{1}{3}\pi r^2 h$. Thus $\frac{V_1}{V_2} = \left(\frac{r_1}{r_2}\right)^2 \left(\frac{h_1}{h_2}\right) \implies \frac{4}{25} = \left(\frac{r_1}{r_2}\right)^2 \times \frac{25}{64} \implies \left(\frac{r_1}{r_2}\right)^2 = \frac{4 \times 64}{25 \times 25} \implies \frac{r_1}{r_2} = \frac{2 \times 8}{5 \times 5} = \frac{16}{25}$.