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A conical vessel whose internal radius i...

A conical vessel whose internal radius is 5 cm and height 24 cm, is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height to which the water rises in the cylindrical vessel.

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Radius of the conical vessel, r = 5 cm.
Height of the conical vessel, h = 24 cm.
Volume of the conical vessel
`=1/3pir^(2)h=(1/3pixx5xx524)cm^(3)=(200pi)cm^(3)`.
Radius of the cylindricla vessel, R = 10 cm.
Let the height to which water rises in teh vessel be H. Then, volume of the water in the cylindrical vessel
`=piR^(2)H=(pixx10xx10xxH)cm^(3)=(100piH) cm ^(3)`.
Volume of the water in cylindrical vessel = volume of the water in the conical vessel
`rArr" "100piH=200pirArrH=200/200=2 cm`.
Hence, the required height is 2 cm.
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