The radius of the base and height of a metallic solid cylinder are r cm and 6 cm respectively. It is melted and recast into a solid cone of the same radius of base. The height of the cone is :

A. 9 cm

B. 18 cm

C. 27 cm

D. 54 cm

Answer: Option B

Solution(By Examveda Team)

Let the height of the cone be h cm
Then,
$$\eqalign{ & \pi \times {r^2} \times 6 = \frac{1}{3} \times \pi \times {r^2} \times h \cr & \Rightarrow h = 18\,cm \cr} $$