Question

A hemispherical bowl of internal radius $18\text{cm}$ is full of fruit juice. The juice is to be filled into cylindrical shaped bottles each of radius $3\text{cm}$ and height $9\text{cm}$. How many bottles are required to empty the bowl?

Answer 1

Given $\Rightarrow$ Radius of hemispherical bowl is $18\text{cm}$

Radius and height of cylindrical bottle is $3\text{cm}$ and $9\text{cm}$ respectively.

To Find $\Rightarrow$ Number of bottles required to empty the hemispherical bowl.

$\text{Volume of hemispherical bowl}=\frac{2}{3}\times \frac{22}{7}\times 18\times 18\times 18{\text{cm}}^3$
$\text{Volume of a cylindrical bottle}=\frac{22}{7}\times 3\times 3\times 9{\text{cm}}^3$

$\begin{array}{cc}No\text{. of bottles}& =\frac{\text{Volume of fruit juice in hemispherical bowl}}{\text{Volume of fruit juice in}1\text{cylindrical bottle}}\\ & =\frac{\frac{2}{3}\times \frac{22}{7}\times 18\times 18\times 18}{\frac{22}{7}\times 3\times 3\times 9}\\ & =48\end{array}$

Hence, the number of bottles required to empty fruit juice present in the hemispherical bowl is equal to $48.$