Volume of two cones are in the ratio 4 : 1 and their diameters are in the ratio 4 : 5. The ratio of their heights is -

25 : 4

Ratio of Volumes = \(\frac{1}{3}\)\(\pi \) r₁²h₁ : \(\frac{1}{3}\)\(\pi \)r₂²h₂ 

                              r₁²h₁         :         r₂²h₂ 

                             (4)²h₁        :          (5)²h₂   = 4  :  1

⇒ h₁ : h₂ = 25 : 4