Q12 of 67 Page 195

A hemispherical bowl of internal radius 9 cm contains liquid. This liquid is to be filled in cylindrical bottles of diameter 3 cm and height 4 cm. How many bottles are required to empty the bowl?

Radius of hemispherical bowl = rh = 9 cm


Diameter of cylindrical bottle = 3 cm


Radius of cylindrical bottle = rc = cm


Height of cylindrical bottle = h = 4 cm


The volume of water is transferred from hemispherical bowl to cylindrical bottles


Suppose there are n bottles then volume of water filled in n bottles will be same as volume of water in hemispherical bowl


Volume of hemisphere = πrh3


Volume of cylinder = πrc2h


⇒ πrh3 = n × πrc2h


⇒ 2rh3 = 3nrc2h


Substitute values


⇒ 2 × 93 = 3n × × 4


⇒ 2 × 93 = 3n × 9


⇒ 2 × 92 = 3n


⇒ 162 = 3n


⇒ n = 54


Therefore, 54 bottles are required to empty the bowl


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