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Question

A hemispehrical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 cylindircal bottles of diameter 6 cm. Find the height of each bottle, if 10% liquid is wasted in this transfer.

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Solution

Internal diameter of hemispherical bowl=36 m

Radius of hemispherical bowl (r)=18 cm

Volume of liquid=23πr3

=23×π×183

Diameter of bottle=6 cm

Radius of bottle=3 cm

Height of bottle be hcm

Now,volume of a cylindrical bottle-πR2h

=π32h

=9πh

Volume of liquid to be transfer=volume of liquoid -10% volume of liquid

=23π18310100(23π183)

=23π183(110100)

=23π183×910

=π×183×35

Number of cylindrical bottles=Volumes of liquid to be transferredVolume of a bottle

72=π×18×18×18×359πh

h=275=5.4 cm

Hence,height of each bottle will be 5.4 cm.


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