Question

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

Answer 1

Let $n$ cylindrical bottles are required to empty the bowl.

For the hemispherical bowl,

$R=15cm$

For the cylindrical bottles,

$r=5cm$

$h=6cm$

So, we can say that volume of $n$ cylindrical bottle is equal to the volume of hemispherical bowl,

$\begin{array}{cc}n\times \pi r^{2}h& =\frac{2}{3}\pi R^3\\ n\times {\left(5\right)}^2\times 6& =\frac{2}{3}\times {\left(15\right)}^3\\ n& =\frac{2\times 15\times 15\times 15}{3\times 5\times 5\times 6}\\ & =15\end{array}$

Hence, $15$ bottles are required to empty the bowl