Correct Answer: Option A

Explanation

Triangles OAD is similar to OBC

\(\frac{\text{OA}}{\text{AD}}\) = OB

But \(\frac{\text{OB}}{\text{BC}}\) = OA + OB

Height of the cone is OB

Let OA = x;

OB = 12 + x

\(\frac{\text{x}}{6}\) = \(\frac{(12 + x)}{12}\)

Hence \(\frac{\text{x}}{6}\) = \(\frac{(12 + x)}{12}\) ⇒ 12x = 6x + 72

6x = 72 ⇒ x = 12 cm

Height of cone is DB = 12 + x = (12 + 12) cm = 24 cm

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