Q. 75.0( 2 Votes )

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.

Answer :

Given.


Height of bucket is 44 cm


Radius of bucket is 21 cm


Height of conical heap is 33 cm


Formula used/Theory.


Volume of cylinder = πr2h


Volume of cone = πr2h


Let the Radius of conical heap be x


Volume of bucket = πr2h


= π × (21 cm)2 × 44 cm


= 19404π cm3


Volume of conical heaps = πr2h


= π × x2 × 33 cm


= 11π × x2 cm


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


As we put bucket of sand on ground it will form a conical heap volume of conical heaps will be equal to volume of bucket


equating both we will get the Radius of conical heap


Volume of bucket = Volume of conical heaps


11π × x2 cm = 19404π cm3


x2 =


x2 = 1764 cm2


x = √ (1764 cm2)


x = 42 cm


Radius of conical heap is 42 cm


In cone;


As the radius , height and slant height makes Right angled triangle where hypotenuse is slant height


Then by Pythagoras theorem


(Slant height)2 = (height)2 + (radius)2


(Slant height)2 = (33 cm)2 + (42 cm)2


(Slant height)2 = 1089 cm2 + 1764 cm2


(Slant height)2 = 2853 cm2


Slant height = √(2853 cm2)


= 53.41 cm


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