The ratio of the of two cones is 5 : 6 and their volumes are in the ratio 8 : 9. The ratio of their height is:

Solution (By Examveda Team)

$$\eqalign{ & {r_1}:{r_2} = 5:6 \cr & {v_1}:{v_2} = 8:9 \cr & \frac{{{v_1}}}{{{v_2}}} = \frac{{\pi r_1^2{h_1}}}{{\pi r_2^2{h_2}}} \cr & \frac{8}{9} = \frac{{25 \times {h_1}}}{{36 \times {h_2}}} \cr & 32:25 = {h_1}:{h_2} \cr} $$