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

25 : 64

Ratio of volumes of cones⇒  \(\frac{1}{3}\) \(\pi \)R₁²H₁ : \(\frac{1}{3}\) \(\pi \)R₂²H₂

⇒ R₁²H₁ : R₂²H₂ = 1   :   4 ...... (i)

Ratio of diameter = Ratio of radius = 4 : 5

In eq. (i) 

⇒ R₁²H₁ : R₂²H₂ = 1 : 4

⇒ (4)² H₁ : (5)² H₂ = 1 :4 

⇒ H₁ : H₂ = \(\frac{1}{4}\) × \(\frac{25}{16}\)

 = 25 : 64