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Question

A hemispherical bowl of internal radius 9cm contains a liquid. This liquid is to be filled into cylindrical-shaped small bottles of diameter 3cm and height 4cm. How many bottles will be needed to empty the bowl?


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Solution

Step 1: Find the volume of the hemispherical bowl

The radius of the hemispherical bowl=9cm

The volume of the hemispherical bowl=23πr3

=23×227×9×9×9=1527.42cm3

Step 2: Find the volume of the cylindrical-shaped bottle

The radius of the cylindrical-shaped bottles=32=1.5cm(Radius is half of the diameter)

The height of the cylindrical-shaped bottles=4cm

The volume of the cylindrical-shaped bottles=πr2h

=227×1.5×1.5×4=28.28cm3

Step 2: Find the number of the cylindrical-shaped bottle

Let n bottles are needed, so the volume of n cylindrical bottles=28.28×n

28.28×n=1527.42n=1527.4228.28n=54

Hence, the number of bottles required is 54.


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