Question

A right circular cone is 3.6 cm high and the radius of its base is 1.6 cm. It is melted and recast into a right circular cone having base radius 1.2 cm. Find its height.

Answer 1

Let the cone which is being melted be denoted by cone 1 and let the cone into which cone 1 is being melted be denoted by cone 2.

Height of cone 1 = 3.6 cm
Radius of the base of cone 1 = 1.6 cm
Radius of the base of cone 2 = 1.2 cm
Let h cm be the height of cone 2.
The volumes of both the cones should be equal.

$$\begin{gathered} \mathrm{i}.\mathrm{e}.,\frac{1}{3}\mathrm{\pi }\times 1.6^2\times 3.6=\frac{1}{3}\mathrm{\pi }\times 1.2^2\times \mathrm{h} \\ \Rightarrow \mathrm{h}=\frac{1.6\times 1.6\times 3.6}{1.2\times 1.2}=6.4\mathrm{cm} \end{gathered}$$

∴ Height of cone 2 = 6.4 cm