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Question

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.

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Solution

The cylinderical bucket has the height H = 32 cm
radius, R = 18 cm
Volume of the cylinderical bucket will be
V=πR2H=π182×32
Height of the conical heap, h = 24 cm
Volume of cylinderical bucket = Volume of the conical heap
πR2H=13πr2h182×32=13r224182×32×324=r21296=r236=r
Hence, the radius of the conical heap = 36 cm
Slant height l=h2+r2l=242+362l=576+1296l=1872l=43.2 cm
Thus, the slant height l = 43.27 cm

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