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 = πr^{2}h

Volume of cone = πr^{2}h

Let the Height of container be x

Radius of cylinder and cone is = 40cm

Volume of container = πr^{2}h

= π × (40 cm)^{2} × x

= 1600πx cm^{2}

Volume of conical heaps = πr^{2}h

= π(40 cm)^{2} × 30 cm

= 16000π cm^{3}

Volume of 45 conical heaps = 45 × 16000π cm^{3}

= 720000π cm^{3}

**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 cm^{2} = 720000π cm^{3}

x =

x = 450 cm

∴ Height of container is 450 cm

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