The radius of two circular cylinders are in the ratio 3 : 2 and the ratio of their volumes is 27 : 16. What is the ratio of their heights?

Solution (By Examveda Team)

$$\eqalign{ & {r_1}:{r_2} = 3:2 \cr & {v_1}:{v_2} = 27:16 \cr & {\text{Height}} \to {h_1}:{h_2} \cr & \frac{{9 \times {h_1}}}{{4 \times {h_2}}} = \frac{{27}}{{16}} \cr & \frac{{{h_1}}}{{{h_2}}} = \frac{3}{4} \cr & {h_1}:{h_2} = 3:4 \cr} $$