A cylindrical bucket of height 32 cm and base radius 18 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 24 cm, find the radius and slant height of the heap.

For cylindrical bucket,


Radius, r = 18 cm


Height, h = 32 cm


As we know,


Volume of cylinder = πr2h


Where r is base radius and h is height of cylinder.


Volume of sand in bucket = π(18)2(32) cm3


Also, For conical heap


Let the radius be r and height, h = 24 cm is given,


As we know,



Where r is base radius and h is height of cone



As the volume of sand is constant


Volume of sand in bucket = Volume of conical heap


π (18)2(32) = 8πr2


(18)(18)(4) = r2


r = 18(2) = 36 cm


Also, we know


l2 = h2 + r2, where h , r and l are height radius respectively.


l2 = (24)2 + (36)2 = 576 + 1296 = 1876


l = 43.267 cm


So, radius and slant height of heap are 36 cm and 43.267 cm respectively.


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