The height of a right circular cone is 30 cm. A small cone is cut off from the top by a plane parallel to the base of the cone. If the volume of the small cone is ​$$\frac{1}{27}$$​ of the volume of the given cone, then at what height above the base was the cone cut?

Correct option is C

Let:
H = 30 cm (Height of the original cone)
h = Height of the small cone
V_small / V_large = (h/H)³ = 1/27
(h / 30)³ = 1/27
Step 2: Solving for h
Taking the cube root on both sides:
(h / 30) = 1/3
h = 30 × 1/3 = 10 cm
Thus, the small cone has a height of 10 cm, meaning it was cut at:
Height from the base = 30 - 10 = 20 cm.