Question

A solid metallic sphere of radius 8 cm is melted and recast into spherical balls each of radius 2 cm. Find the number of spherical balls obtained.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{solid}\mathrm{metallic}\mathrm{sphere},R=8\mathrm{cm}\mathrm{and} \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{spherical}\mathrm{ball},r=2\mathrm{cm} \\ \mathrm{Now}, \\ \mathrm{The}\mathrm{number}\mathrm{spherical}\mathrm{balls}\mathrm{obtained}=\frac{\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{solid}\mathrm{metallic}\mathrm{sphere}}{\mathrm{Volume}\mathrm{of}\mathrm{a}\mathrm{spherical}\mathrm{ball}} \\ =\frac{\left({\displaystyle \frac{4}{3}}\mathrm{\pi }{R}^3\right)}{\left({\displaystyle \frac{4}{3}}\mathrm{\pi }{r}^3\right)} \\ ={\left(\frac{R}{r}\right)}^3 \\ ={\left(\frac{8}{2}\right)}^3 \\ =4^3 \\ =64 \end{gathered}$$

So, the number of spherical balls obtained is 64.