Q. 25.0( 2 Votes )

A cylindrical container having diameter 16 cm and height 40 cm is full of ice - cream. The ice - cream is to be filled into cones of height 12 cm and diameter 4 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with the ice - cream.

Answer :

Given.


Radius of Hemispherical bowl and cone is = 2 cm


Cylindrical container of diameter 16 cm and height 40 cm


Formula used/Theory.


Volume of Cylinder = πr2h


Volume of hemisphere = πr3


Volume of Cone = πr2h


Volume of ice - cream will be equal to sum of volume of hemisphere bowl and volume of cone


Volume of hemisphere = πr3


= × π × (2 cm) 3


= π cm3


Volume of Cone = πr2h


= × π × (2 cm) 2 × 12 cm


16π cm3


Volume of ice - cream = 16π cm3 + π cm3


= × 16π cm3


Radius of container = = 8 cm


Volume of container = πr2h


= π × (8cm) 2 × 40 cm


= 2560π cm3


**Note we will not put value of π as it will be divided in next step


Number of ice - cream will be dividing the total volume of ice - cream in container by volume of ice - cream contained by 1 cone


Number of ice - creams =


= 120


120 ice - cream can be filled by the container


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