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
$$\begin{gathered} \frac{VolumeofthehemisphericalBowl}{Volumeofthecylindericalbottles}=n \\ \Rightarrow \frac{{\displaystyle \frac{2}{3}{\mathrm{\pi R}}^3}}{{\mathrm{\pi r}}^2\mathrm{h}}=n \\ \Rightarrow \frac{\frac{2}{3}{{\displaystyle \left(9\right)}}^3}{{{\displaystyle \left(1.5\right)}}^2{\displaystyle \left(4\right)}}=n \\ \Rightarrow 54=n \end{gathered}$$
Hence, the 54 bottles are required.