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Question -

A cylindrical bucket, 32 cm high and 18 cm of radius of the base, 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.



Answer -

Given,

Height of thecylindrical bucket = 32 cm

Radius of thecylindrical bucket = 18 cm

Height of conical heap= 24 cm

We know that,

Volume of cylinder = ╧А├Ч r2┬а├Ч h

And, volume of cone =1/3 ╧А ├Ч r2┬а├Ч h

Then, from thequestion

Volume of the conicalheap = Volume of the cylindrical bucket

1/3 ╧А ├Ч r2┬а├Ч24 = ╧А ├Ч 182┬а├Ч 32

r2┬а=182┬аx 4

r = 18 x 2 = 36 cm

Now,

Slant height of theconical heap (l) is given by

l = тИЪ(h2┬а+r2)

l = тИЪ(242┬а+362) = тИЪ1872

l = 43.26 cm

Therefore, the radiusand slant height of the conical heap are 36 cm and 43.26 cm respectively.

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