Question

A hemispherical bowl of internal radius $9\mathrm{cm}$ is full of liquid. The liquid is to be filled into cylindrical shaped small bottles each of diameter $3\mathrm{cm}$ and height $4\mathrm{cm}$. How many bottles are needed to empty the bowl?

Answer 1

Step 1: Determine the number of required cylindrical bottles.

$\begin{array}{rcl}Numberofbottles& =& \frac{\text{Volume of hemispherical bowl}}{\text{Volume of one cylindrical bottle}}\\ & =& \frac{\frac{2}{3}\pi r^3}{\pi R^{2}h}\\ & =& \frac{\frac{2}{3}\times \pi \times 9\times 9\times 9}{\pi \times 1.5\times 1.5\times 4}\\ & =& 54\end{array}$

Hence, the number of required cylindrical bottles is $54$