Question

A solid sphere of radius 3 cm is melted and then cast into smaller spherical balls, each of diameter 0.6 cm. Find the number of small balls thus obtained.

Answer 1

Radius of the solid sphere = 3 cm

Volume of the solid sphere = $\frac{4}{3}\mathrm{\pi }{r}^3$
= $\frac{4}{3}\times \frac{22}{7}\times 3^3{\mathrm{cm}}^3$

Diameter of the spherical ball = 0.6 cm
Radius of the spherical ball = 0.3 cm

Volume of the spherical ball = $\frac{4}{3}\times \frac{22}{7}\times {\left(0.3\right)}^3{\mathrm{cm}}^3$

Now, number of small spherical balls = $\frac{\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{sphere}}{\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{spherical}\mathrm{ball}}$
$$\begin{gathered} =\frac{{\displaystyle \frac{4}{3}}\mathrm{\pi }\times 27}{{\displaystyle \frac{4}{3}}\mathrm{\pi }\times \left(0.3^3\right)} \\ =1000 \end{gathered}$$

∴ The number of small balls thus obtained is 1000