A hemispherical bowl of internal diameter 30 cm contains some liquid. This liquid is to be poured into cylindrical bottles of diameter 5 cm and height 6 cm each. Find the number of bottles required.
Inner diameter of the bowl $=30 \mathrm{~cm}$
Inner radius of the bowl $=\frac{30 \mathrm{~cm}}{2}=15 \mathrm{~cm}$
Inner volume of the bowl $=$ Volume of liquid $=\frac{2}{3} \pi r^{3}=\frac{2}{3} \times \pi \times 15^{3} \mathrm{~cm}^{3}$
Radius of each bottle $=2.5 \mathrm{~cm}$
Height $=6 \mathrm{~cm}$
Volume of each bottle $=\pi \mathrm{r}^{2} \mathrm{~h}=\pi \times \frac{5}{2} \times \frac{5}{2} \times 6=\frac{75 \pi}{2} \mathrm{~cm}^{3}$
Total number of bottles required $=\frac{\left[\frac{2}{3} \pi \times 15 \times 15 \times 15\right]}{\frac{75 \pi}{2}}=\frac{2 \pi \times 15 \times 15 \times 15 \times 2}{3 \times 75 \pi}=15 \times 4=60$