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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