Q. 65.0( 2 Votes )

There are 45 conical heaps of wheat, each of them having diameter 80 cm and height 30 cm. To store the wheat in a cylindrical container of the same radius, what will be the height of cylinder?

Answer :

Given.


Height of cone is 30 cm


Cone and cylinder of diameter 80 cm


Formula used/Theory.


Volume of cylinder = πr2h


Volume of cone = πr2h


Let the Height of container be x


Radius of cylinder and cone is = 40cm


Volume of container = πr2h


= π × (40 cm)2 × x


= 1600πx cm2


Volume of conical heaps = πr2h


= π(40 cm)2 × 30 cm


= 16000π cm3


Volume of 45 conical heaps = 45 × 16000π cm3


= 720000π cm3


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


As we put 45 conical heaps of wheat in cylindrical container volume of 45 conical heaps will be equal to volume of container


equating both we will get the Height of container


Volume of container = Volume of 45 conical heaps


1600π × x cm2 = 720000π cm3


x =


x = 450 cm


Height of container is 450 cm


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