A hemispherical bowl of internal radius $ 9 \mathrm{~cm} $ is full of liquid. This 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 necessary to empty the bowl?

Given:

A hemispherical bowl of internal radius \( 9 \mathrm{~cm} \) is full of liquid. This liquid is to be filled into cylindrical shaped small bottles each of diameter \( 3 \mathrm{~cm} \) and height \( 4 \mathrm{~cm} \).

To do:

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

Solution:

Radius of the hemisphere bowl $R=9 \mathrm{~cm}$

Volume of the liquid filled in it $=\frac{2}{3} \pi R^{3}$

$=\frac{2}{3} \pi(9)^{3}$

$=486 \pi \mathrm{cm}^{3}$

Diameter of each cylindrical bottle $=3 \mathrm{~cm}$

This implies,

Radius of each cylindrical bottle $r=\frac{3}{2} \mathrm{~cm}$

Height of each cylindrical bottle $h=4 \mathrm{~cm}$

Therefore,

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

$=\pi(\frac{3}{2})^{2} \times 4$

$=\frac{9}{4} \pi \times 4$

$=9 \pi \mathrm{cm}^{3}$

Number of bottles required to fill the liquid of the bowl $=$ Volume of the liquid in hemisphere bowl $\div$ Volume of each cylindrical bottle

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

$=54$

The number of bottles necessary to empty the bowl is $54$.

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Updated on: 10-Oct-2022

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