Question

A hemispherical bowl of internal radius 9 cm  is full of liquid . The liquid is to be filled into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm . How many bottles  are needed to empty the bowl ?

Answer 1

The radius of the hemispherical bowl, R = 9 cm
Radius of the cylinderical bottles, r = 1.5 cm
Height of the bottles, h = 4 cm
Let the number of bottles required be n. 
Volume of the hemispherical bowl = n × Volume of the cylinderical bottles

$$\frac{\text{ Volume of the hemispherical Bowl}}{\text{ Volume of the cylinderical bottles}}=n$$

$$\Rightarrow \frac{\frac{2}{3}\pi R^3}{\pi r^{2}h}=n$$

$$\Rightarrow \frac{\frac{2}{3}{\left(9\right)}^3}{{(1.5)}^2\left(4\right)}=n$$

$$\Rightarrow 54=n$$

Hence, the 54 bottles are required.