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Question
A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged, then the water level rises by ______.
Options
3 cm
4 cm
5 cm
6 cm
Solution
Radius of the sphere , `"r" = 18/2 =9 "cm" ` and
Radius of the cylindrical vessel, `"R" = 36/2 = 18 "cm"`
Let the rise of water level be H.
Now,
Volume of the water rised = Volume of the sphere
`=> pi"R"^2"h" = 4/3 pi"r"^3`
`=> "h" = (4pi"r"^3)/(3"R"^2)`
`=> "h" = (4xx9xx9xx9)/(3xx18xx18)`
∴ h = 3 cm
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