Question:
How many lead balls, each of radius 1 cm, can be made from a sphere of radius 8 cm?
Solution:
Radius of the sphere $=R=8 \mathrm{~cm}$
Volume of the sphere $=\frac{4}{3} \pi R^{3}=\frac{4}{3} \pi \times 8 \times 8 \times 8=\frac{4}{3} \pi \times 512 \mathrm{~cm}^{3}$
Radius of each new ball $=r=1 \mathrm{~cm}$
Volume of each ball $=\frac{4}{3} \pi \mathrm{r}^{3}=\frac{4}{3} \pi \times 1 \times 1 \times 1=\frac{4}{3} \pi \times 1 \mathrm{~cm}^{3}$
Total number of new balls that can be made $=\frac{\text { Volume of sphere }}{\text { Volume of each ball }}=\frac{\frac{4}{3} \pi \times 512}{\frac{4}{3} \pi \times 1}=512$