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Question

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


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Solution

Step 1: Find the volume of hemispherical bowl

The internal diameter of the hemispherical bowl=36cm

The internal radius of the hemispherical bowl=362=18cm(Radius is half of the diameter)

The volume of the hemispherical bowl=23πr3

23×227×18×18×18=12219.43cm3

Step 2: Find the height of cylindrical bottles

The diameter of the cylindrical bottle=6cm

The radius of the cylindrical bottle=62=3cm

The volume of the one cylindrical bottle=πr2h

227×3×3×h=1987h

The volume of the 72cylindrical bottle=72×1987h

If 10% of the liquid is wasted in this transfer, then 10% of 12219.43=10100×12219.43=1221.943

The remaining volume of the liquid=12219.43-1221.943=10997.487cm3

72×1987h=10997.487h=10997.487×772×198=5.4cm

Therefore, the height (h) of each bottle is 5.4cm.


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