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Question 7
A cylindrical bucket, 32 cm high and with radius of base 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

Radius of cylinder = 18 cm, height = 32 cm
Height of cone = 24 cm
Volume of cylinder
=πr2h
=π×182×32
Volume of cone = Volume of cylinder
Volume of cone
=13πr2×24
Hence, radius of cone can be calculated as follows:
r2=3×π×182×32π×24
Or r2=182×22
Or,r=36 cm
Now, slant height of conical heap can be calculated as follows:
l=h2+r2
=242+362
=576+1296
=1872=1213 cm

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