Let V₁ be the volume of first cone and V₂ be the volume of second cone.

Then, V₁:V₂ = 1:4

Let d₁ be the diameter of first cone and d₂ be the diameter of second cone.

Then d₁:d₂ = 4:5

Let h₁ be the height of first cone and h₂ be the height of second cone.

We know that volume of cone is given by V = 1/3 × π(d²/4)h

∴

⇒

⇒

⇒

⇒

∴ h₁:h₂ = 25:64

∴ Ratio of height of two cones is 25:64.