A hemispherical bowl of internal radius $ 9 \mathrm{~cm} $ is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius $ 1.5 \mathrm{~cm} $ and height $ 4 \mathrm{~cm} $. How many bottles are needed to empty the bowl?

Given:

A hemispherical bowl of internal radius \( 9 \mathrm{~cm} \) is full of liquid.

The liquid is to be filled into cylindrical shaped bottles each of radius \( 1.5 \mathrm{~cm} \) and height \( 4 \mathrm{~cm} \).

To do:

We have to find the number of bottles needed to empty the bowl.

Solution:

Radius of the hemispherical bowl $r = 9\ cm$

Volume of liquid in the hemispherical bowl $=\frac{2}{3} \pi r^{3}$

$=\frac{2}{3} \pi \times 9^3$

$=486 \pi$

Radius of each cylindrical bottle $R = 1.5\ cm$

Height of each cylindrical bottle $h = 4\ cm$

Volume of each cylindrical bottle $=\pi \mathrm{R}^{2} h$

$=\pi \times (1.5)^2 \times 4$

$=9 \pi$

Number of cylindrical bottles needed to empty the bowl $=\frac{\text { Volume of hemisphere bowl }}{\text { Volume of one cylindrical bottle }}$

$=\frac{486 \pi}{9 \pi}$

$=54$

Hence, 54 bottles are needed to empty the bowl.