A solid sphere of radius 3 cm is melted and then cast into small spherical balls, each of diameter 0.6 cm.

Radius of solid sphere $=3 \mathrm{~cm}$

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

Radius of each new ball $=0.3 \mathrm{~cm}$

Volume of each new ball $=\frac{4}{3} \pi \mathrm{r}^{3}=\frac{4}{3} \pi \times \frac{3}{10} \times \frac{3}{10} \times \frac{3}{10} \mathrm{~cm}^{3}$

Total number of balls $=\frac{\frac{4}{3} \pi \times 3 \times 3 \times 3}{\frac{4}{3} \pi \times \frac{3}{10} \times \frac{3}{10} \times \frac{3}{10}}=1000$