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Question
A cylindrical vessel 32 cm high and 18 cm as the 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, the radius of its base is
Options
12 cm
24 cm
36 cm
48 cm
Solution
Volume of sand filled in cylindrical vessel
`= pi(18)^2 xx 32`
`= 32 xx 324 pi`
Clearly,
The volume of conical heap = volume of sand
`1/3 pir^2 xx 24 = 32 xx 324 pi`
`r^2 = (32 xx 324)/8`
`r = sqrt(4 xx 324)`
`r = 2 xx 18`
`= 36`
`r = 36 cm`
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