Q. 65.0( 1 Vote )

A hemisphere bowl of internal diameter 30 cm is full of a liquid. This liquid is filled into cylindrical - shapes bottles each of diameter 5 cm and height 6 cm. How many bottles are required?

Answer :

Given: diameter of hemisphere = 30 cm


Radius of hemisphere = rh = 30/2 = 15cm


Diameter of cylindrical shaped bottles = 5 cm


radius of cylindrical shaped bottles = 5/2 = rc = 2.5 cm


Height of cylindrical shaped bottle = h = 6 cm


Formula: volume of hemisphere = (volume of sphere/2) = (2/3)πrh3


Volume of cylinder = πrc2h


Let ‘n’ bottles are required


As we are filling the cylindrical bottles with liquid in hemispherical bowl hence we can say that


volume of liquid in cylindrical bottles = volume of liquid in hemisphere


n × π × rc2 × h = (2/3) × π × rh3


n × 2.52 × 6 × 3 = 2 × 153


n × 6.25 × 9 = 3375


n = 3375/56.25


n = 60


Therefore 60 cylindrical shaped bottles are required to fill the liquid from hemispherical bowl.


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