Question

A hemispherical bowl of internal diameter $30\mathrm{cm}$ contains some liquid. This liquid is to be filled into cylindrical shaped bottles each of diameter $5\mathrm{cm}$ and height $6\mathrm{cm}$. Find the number of bottles necessary to empty the bowl.

Answer 1

Step 1: Determine the number of bottles necessary to empty the bowl.

$\begin{array}{rcl}Numberofbowl& =& \frac{Volumeofhemisphere}{Volumeofcylinder}\\ & =& \frac{{\displaystyle \frac{2}{3}}{\mathrm{\pi r}}^3}{\mathrm{\pi }{\left(\mathrm{r}\text{'}\right)}^2\mathrm{h}}\\ & =& \frac{2r^3}{3{\left(\mathrm{r}\text{'}\right)}^2\mathrm{h}}\\ & =& \frac{2\times {\displaystyle \frac{30}{2}}\times {\displaystyle \frac{30}{2}}\times {\displaystyle \frac{30}{2}}}{3\times {\displaystyle \frac{5}{2}}\times {\displaystyle \frac{5}{2}}\times 6}\\ & =& 60\end{array}$

Hence, the number of bottles necessary to empty the bowl is $60$.