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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