Question

22) A hemispherical bowl of internal radius 9cm is full of a liquid. This liquid is to be filled into Small cylindrical bottles of diameter 3cm and
height 4cm each. Find the minimum number of bottles required to empty the bowl​

Answer 1

Answer:

54

Step-by-step explanation:

volume will be same so equated them. kindly see the attachment

Answer 2

Answer:

The minimum number of bottles required to empty the bowl is 54.

Step-by-step-explanation:

We have given that,

A hemispherical bowl is full of liquid. And this liquid is to be filled in small cylindrical bottles.

For hemispherical bowl -

• Radius ( R ) = 9 cm

For cylindrical bottles -

• Diameter ( d ) = 3 cm
• Height ( h ) = 4 cm

We know that,

Radius is half of the diameter.

$\therefore\sf\:r\:=\:\dfrac{d}{2}$

$\implies\sf\:r\:=\:\dfrac{3}{2}$

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

It means we have to divide the volume of hemispherical bowls by the volume of cylindrical bottles.

We know that,

$\pink{\sf\:Volume\:of\:hemisphere\:=\:\dfrac{2}{3}\:\pi\:R^3}\sf\:\:-\:-\:[\:Formula\:]$

$\pink{\sf\:Volume\:of\:cylinder\:=\:\pi\:r^2\:h}\sf\:\:-\:-\:[\:Formula\:]$

$\displaystyle{\therefore\sf\:Number\:of\:bottles\:=\:\dfrac{Volume\:of\:hemispherical\:bowls}{Volume\:of\:cylindrical\:bottles}}$

$\implies\sf\:N_b\:=\:\dfrac{\dfrac{2}{3}\:\cancel{\pi}\:R^3}{\cancel{\pi}\:r^2\:h}$

$\implies\sf\:N_b\:=\:\dfrac{\dfrac{2}{3}\:\times\:9\:\times\:9\:\times\:9}{\dfrac{3}{2}\:\times\:\dfrac{3}{2}\:\times\:4}$

$\implies\:\:\!\!$$\!\!\sf\:N_b\:=\:\dfrac{2}{\cancel3}\:\times\:\cancel{9} \:\times\:\cancel{9}\:\times\:\cancel{9}\:\times\:\dfrac{2}{\cancel3}\:\times\:\dfrac{2}{\cancel3}\:\times\:\dfrac{1}{4}$

$\displaystyle{\implies\sf\:N_b\:=\:\dfrac{2\:\times\:3\:\times\:3\:\times\:3\:\times\:2\:\times\:2}{4}}$

$\implies\sf\:N_b\:=\:\dfrac{2\:\times\:3\:\times\:3\:\times\:3\:\times\:\cancel{4}}{\cancel4}$

$\implies\sf\:N_b\:=\:3\:\times\:3\:\times\:3\:\times\:2$

$\implies\sf\:N_b\:=\:27\:\times\:2$

$\implies\boxed{\red{\sf\:No.\:of\:bottles\:=\:54}}$

The minimum number of bottles required to empty the bowl is 54.

$\rule{200}{1}$

Additional Information:

1. Hemisphere:

When a sphere is divided into two equal parts, a hemisphere is formed.

2. Formulae related to hemisphere:

$\longrightarrow\pink{\sf\:1.\:Area\:of\:base\:=\:\pi\:r^2}$

$\longrightarrow\red{\sf\:2.\:Curved\:surface\:area\:=\:2\:\pi\:r^2}$

$\longrightarrow\blue{\sf\:3.\:Total\:surface\:area\:=\:3\:\pi\:r^2}$

$\longrightarrow\green{\sf\:4.\:Volume\:=\:\dfrac{2\:\pi\:r^3}{3}}$

3. Formulae related to cylinder:

$\longrightarrow\pink{\sf\:1.\:Area\:of\:base\:=\:\pi\:r^2}$

$\longrightarrow\red{\sf\:2.\:Curved\:surface\:area\:=\:2\:\pi\:r\:h}$

$\longrightarrow\blue{\sf\:3.\:Total\:surafce\:area\:=\:2\:\pi\:r\:(\:r\:+\:h\:)}$

$\longrightarrow\green{\sf\:4.\:Volume\:=\:\pi\:r^2\:h}$