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A Hemisphere Tool of Internal Radius 9cm is Full of Liquid. this Liquid is to Be Filled into Cylindrical Shaped Small Bottles Each of Diameter 3cm and Height 4cm. How Many Bottles Are Necessary - Mathematics

Answer in Brief

A hemisphere tool of internal radius 9cm is full of liquid. This liquid is to be filled into
cylindrical shaped small bottles each of diameter 3cm and height 4cm. how many bottles are necessary to empty the bowl.

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Solution

Given that internal radius of hemisphere bowl = 90m

Volume of hemisphere `=3/4pir^3`

`=2/3xxpi(9)^3`          ______(1)

Given diameter of cylindrical bottle = 3cm

Radius`=3/2cm`

Height = 4cm

Volume of cylindrical = πr2h

`=pi(3/2)^2xx4`   ______(2)

Volume of hemisphere bowl is equal to volume sum of n cylindrical bottles

(1) = (2)

`2/3pi(9)^3=pi(3/2)^2xx4xxn`

⇒`n=(2/3pi(9)^3)/(pi(3/2)^2xx4)`

⇒ n = 54

∴ No of bottles necessary to empty the bottle = 54.

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