**Question:**

A hemispherical bowl of internal radius 9 cm is full of water. This water is to be filled in cylindrical bottles of diameter 3 cm and height 4 cm. Find the number of bottles needed in which the water can be filled.

**Solution:**

Radius of hemisphere = 9 cm.

Volume of hemisphere $=\frac{2}{3} \pi \mathrm{r}^{3}$

$=\left(\frac{2}{3} \pi \times 9 \times 9 \times 9\right) \mathrm{cm}^{3}$

Radius of each bottle $=\frac{3}{2} \mathrm{~cm}$

Height of each bottle $=4 \mathrm{~cm}$

Volume of each bottle $=\pi r^{2} h$

$=\left(\pi \times \frac{3}{2} \times \frac{3}{2} \times 4\right) \mathrm{cm}^{3}$

Number of bottles $=\frac{\text { Volume of the hemisphere }}{\text { Volume of each bottle }}$

$=\frac{2 \pi \times 9 \times 9 \times 9 \times 2 \times 2}{3 \times \pi \times 3 \times 3 \times 4}$

$=54$