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Let the Height and Radius of the Big cone be H cm and R cm

And of small cone be h cm and r cm

Let the volume of the big cone be V and of small cone be v

The cone is cut from the big cone then , they both cones would be similar to each other and according to the property of the similarity ,

H/R = h/r

⇒ h= Hr/R

⇒ h = 30 r/R ...............................eqn 1

Volume of the cone = 1/3 πr²h

v/V = r²h/R²H = 1/27

⇒ r²h = 30 R²/27

⇒ h=10 R²/9 r² ........................... eqn 2

On substituting the value of the h from eqn 1 in eqn 2 we get : -

30r/R = 10R²/9r²

⇒ r³/R³ = 1/27

⇒ r/R = 1/3

Substituting this ratio in eqn 1 we get :-

h = 30 × 1/ 3

⇒ __h = 10 cm Ans.__

Hence, Height of the small(cut) cone is 10 cm Ans.

And the Height of the Frustum is 30-10 = 20 cm Ans.

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