If the volume of two right circular cones are in the ratio 1 : 3 and their diameters are in the ratio 3 : 5, then the ratio of their heights is?

Let diameter, radius and height of first cone are d₁, r₁ and h₁, respectively and that of second cone are d₂, r₂ and h₂, respectively.
r₁/r₂ = d₁/d₂ = 3/5,
h₁/h₂ = ?
Given,
[(1/3)πr²₁h₁] / [(1/3)πr²₂h₂] = 1/3
⇒ (3/5)² x h₁/h₂ = 1/3
⇒ h₁/h₂ = (1/3) x (25/9) = 25/27