Question

A hemispherical bowl of internal diameter $36cm$ contains a liquid. This liquid is to be filled in cylindrical bottles of radius $3cm$ and height $6cm$. How many bottles are required to empty the bowl?

Answer 1

We have
Radius of hemispherical bowl$=\frac{36}{2}=18cm$

Volume of hemispherical bowl$=\frac{2}{3}\pi \times {\left(18\right)}^3{cm}^3[V=\frac{2}{3}\pi r^3]$

Radius of a cylindrical bottle $=3cm$
Height of a cylindrical bottle $=6cm$

Volume of a cylindrical bottle $=(\pi \times 3^2\times 6){cm}^3$ ....... $v=\pi r^{2}h$
Suppose $x$ bottles are required to empty the bowl
Volume of $x$ cylindrical bottles $=(\pi \times 9\times 6\times x){cm}^3$

Clearly volume of liquid in $x$ bottles = Volume of bowl
$\Rightarrow \pi \times 9\times 6\times x=\frac{2}{3}\pi \times {\left(18\right)}^3$

$\Rightarrow x=72$

$\therefore$ Bottles required to empty the bowl$=72$