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Question
A conical vessel whose internal radius is 10 cm and height 48 cm is full of water. Find the volume of water. If this water is poured into a cylindrical vessel with internal radius 20 cm, find the height to which the water level rises in it.
Solution
Radius of conical vessel r = 10 cm
Height of conical vessel h = 48 cm
The volume of water = volume of conical vessel.
`=1/3 pir^2 h`
`= 1/3pi xx 100 xx 48`
` = 1600pi cm^3`
`1600 xx 3.14`
` = 5024 cm^3`
Let h' be the height of cylindrical vessel, which filled by the water of conical vessel,
Radius of cylindrical vessel = 20 cm
Clearly,
Volume of cylindrical vessel = volume of water
`pi xx (20)^2 xx h = 1600 pi`
` h =(1600)/400`
` h = 4 cm`
Thus, the volume of the cylindrical vessel and height of cylindrical vessel are `5024 cm^3` and 4cm respectively.
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