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   

Answer 1

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