Q7 of 48 Page 267

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.

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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