Question

A hemispherical bowl of internal radius $15\mathrm{cm}$ contains a liquid. The liquid is to be filled into cylindrical shaped bottles of diameter $5\mathrm{cm}$ and height $6\mathrm{cm}$. How many bottles are necessary to empty the bowl?

Answer 1

Step 1: Determine the number of the cylindrical bowls.

Let $x$ represents the number of the cylindrical bowl.

$\begin{array}{rcl}x\times Volumeofcylinder& =& Volumeofhemisphere\\ x\times \mathrm{\pi }{\left(\mathrm{r}\text{'}\right)}^2\mathrm{h}& =& \frac{2}{3}{\mathrm{\pi r}}^3\\ \mathrm{x}\times {\left(\mathrm{r}\text{'}\right)}^2\mathrm{h}& =& \frac{2}{3}{\mathrm{r}}^3\\ \mathrm{x}& =& \frac{2{\mathrm{r}}^3}{3{\left(\mathrm{r}\text{'}\right)}^2\mathrm{h}}\\ \mathrm{x}& =& \frac{2\left(15\right)\times \left(15\right)\times \left(15\right)}{3\left(\frac{5}{2}\right)\times \left(\frac{5}{2}\right)\times 6}\\ & =& 60\end{array}$

Hence, there are $60$ number of a cylindrical bowls formed.