A hemispherical bowl of internal diameter 36 cm contains water. This water is to be filled in cylindrical bottles, each of radius 3 cm and height 6 cm. How many bottles are required to empty the bowl?

Given,

Internal radius of hemispherical bowl, R = $\dfrac{\text{diameter}}{2} = \dfrac{36}{2}$ = 18 cm

Radius of cylindrical bottles, r = 3 cm

Height of the cylindrical bottles, h = 6 cm

Let number of cylindrical bottles needed be n.

∴ Volume of hemispherical bowl = n × Volume of each cylindrical bottle

$\Rightarrow \dfrac{2}{3}π\text{R}^3 = \text{n} \times π\text{r}^2\text{h} \\[1em] \Rightarrow \dfrac{2}{3}\text{R}^3 = \text{n} \times \text{r}^2\text{h} \\[1em] \Rightarrow \dfrac{2}{3} \times 18^3 = \text{n} \times 3^2 \times 6 \\[1em] \Rightarrow \dfrac{2}{3} \times 5832 = \text{n} \times 9 \times 6 \\[1em] \Rightarrow \dfrac{11664}{3} = \text{n} \times 54 \\[1em] \Rightarrow \text{n} = \dfrac{11664}{3 \times 54} \\[1em] \Rightarrow \text{n} = \dfrac{11664}{162} \\[1em] \Rightarrow \text{n} = 72$

Hence, 72 bottles are required to empty the bowl.