Question

A right circular cone is $5.4cm$ high and the radius of its base is $2cm$.

It is melted and recast into another right circular one with a radius of base as $1.5cm$. find the height of the new cone formed.

Answer 1

The volume of the old cone = volume of the new cone

$$\begin{gathered} \frac{1}{3}\mathrm{\pi }\times {{\mathrm{r}}_1}^2{\mathrm{h}}_1=\frac{1}{3}\mathrm{\pi }\times {{\mathrm{r}}_2}^2{\mathrm{h}}_2 \\ {{\mathrm{r}}_1}^2{\mathrm{h}}_1={{\mathrm{r}}_2}^2{\mathrm{h}}_2 \\ {2}^2\times 5.4={\left(1.5\right)}^2\times {\mathrm{h}}_2 \\ {\mathrm{h}}_2=\frac{4\times 5.4}{2.25} \\ =\frac{21.6}{2.25} \\ {\mathrm{h}}_2=9.6\mathrm{cm} \end{gathered}$$

Therefore, the height of the new cone is $9.6cm$