Given height of the cone = 30 cm

Let the small cone is cut off at height h from the top.

Let radius of big cone is r₁ and small cone is r₂

Now volume of the cone V = (1/3)*Π*r² h

Now volume of the big cone V₁ = (1/3)*Π*r₁² h

                                                = (1/3)*Π*r₁² *30

                                                = 10Π*r₁²

Again volume of the big cone V₂ = (1/3)*Π*r₂² h

                                                = (1/3)*Π*r₂² *h

Now according to the question,

      V₂ = V₁ /27

=> V₂ /V₁ = 1/27

=> ((1/3)*Π*r₂² *h)/(10Π*r₁² ) = 1/27

=> ((1/3)*r₂² *h)/(10*r₁² ) = 1/27

=> (r₂² *h)/(30*r₁² ) = 1/27

=> (r₂² )/(r₁² ) * (h/30) = 1/27 .............1

Now from the figure,

Since ΔAPE ∼ ΔAOC    (From AA similarity criterion)

So r₂ /r₁ = h/30

From equation 1

(h/30)² * (h/30) = 1/27

=> (h/30)³ = 1/27

=> (h/30)³ = (1/3)³

=> h/30 = 1/3

=> h = 30/3

=> h = 10

Thus at height 30-10 = 20 cm above the base, a small cone is cut