Question

A metalic solid cone is melted to form a solid cylinder of equal radius. If the height of the cylinder is 6 cm, then the height of the cone was
(a) 10 cm
(b) 12 cm
(c) 18 cm
(d) 24 cm [CBSE 2014]

Answer 1

Let the height of the cone be h.
Volume of cylinder = Volume of cone
$$\begin{gathered} \Rightarrow \mathrm{\pi }{r}^2\left(6\right)=\frac{1}{3}\mathrm{\pi }{r}^{2}h \\ \Rightarrow h=18\mathrm{cm} \end{gathered}$$

Hence, the correct answer is option C.