Q6 of 48 Page 267

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?

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


More from this chapter

All 48 →
4

A cylinder of radius 2 cm and height 10 cm is melted into small spherical balls of diameter 1 cm. Find the number of such balls.

 5

A metallic sphere of radius 15 cm is melted and a wire of diameter 1 cm is drawn from it. Find the length of the wire.

 7

A cylindrical bucket, 44 cm high and having radius of base 21 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 33 cm, find the radius and the slant height of the heap.

 1

A metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The total vertical height of the bucket is 40 cm and that of cylindrical base is 10 cm, radii of two circular ends are 60 cm and 20 cm. Find the area of the metallic sheet used. Also find the volume of water the bucket can hold. (π = 3.14)