Question:
A spherical ball of diameter 21 cm is melted and recast into cubes, each of side 1 cm. Find the number of cubes so formed.
Solution:
Diameter of the spherical ball= 21 cm
Radius of the ball $=\frac{21}{2} \mathrm{~cm}$
Volume of spherical ball $=\frac{4}{3} \pi \mathrm{r}^{3}=\frac{4}{3} \times \frac{22}{7} \times \frac{21}{2} \times \frac{21}{2} \times \frac{21}{2}=11 \times 21 \times 21=4851 \mathrm{~cm}^{3}$
Volume of each cube $=1^{3}=1 \mathrm{~cm}^{3}$
Number of cubes $=\frac{\text { Volume of spherical ball }}{\text { Volume of each cube }}=\frac{4851}{1}=4851$