Question

A metallic cone of radius 12 cm and height 24 cm is melted and made into spheres of radius 2 cm each. How many spheres are formed?

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{metallic}\mathrm{cone},r=12\mathrm{cm}, \\ \mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{metallic}\mathrm{cone},h=24\mathrm{cm}\mathrm{and} \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{sphere},R=2\mathrm{cm} \\ \mathrm{Now}, \\ \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{spheres}\mathrm{so}\mathrm{formed}=\frac{\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{metallic}\mathrm{cone}}{\mathrm{Volume}\mathrm{of}\mathrm{a}\mathrm{sphere}} \\ =\frac{\left({\displaystyle \frac{1}{3}}\mathrm{\pi }{r}^{2}h\right)}{\left({\displaystyle \frac{4}{3}}\mathrm{\pi }{R}^3\right)} \\ =\frac{r^{2}h}{4R^3} \\ =\frac{12\times 12\times 24}{4\times 2\times 2\times 2} \\ =108 \end{gathered}$$

So, the number of spheres so formed is 108.