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A hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 3 cm and height 4 cm. The number of bottles required to empty the bowl is ____.

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Detailed Solution

A hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 3 cm and height 4 cm. The number of bottles required to empty the bowl is 54.
Given,
Internal radius of a hemispherical bowl = 9 cm.
Diameter of cylindrical shaped small bottles = 3 cm.
So, radius would be = 1.5 cm.
Height of cylindrical shaped small bottles = 4 cm.
Volume of hemisphere is,

= 23 π r 3 = 23 × π × (9) 3 = 486 π

Now, the volume of cylindrical bottle is,

= π r 2 h = π 1.5 2 (4) = 9 π

Now, the number of bottles is,
= volume of hemispherical bowl

÷

volume of one cylindrical bottle

= 486 π 9 π = 4869 = 54

Hence, the number of bottles is 54.

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