There is some water in a cylindrical vessel of diameter 12 cm. A solid metallic spere of redius 4 cm is dropped in to it . Find the increase in height of the water surface if sphere is fully immersed in to the water.

Answer

200pi `cm^(3)` and210 `pi cm^(2)`

Explanation

Radius of sphere = 4cm
Volume of sphere=`(4)/(3)pi(4)^(3)=(256pi)/(3)cm^(3)`
For cylindrical vessel,
`radius r=(12)/(2)=6cm`
Let h be the increase in height of the waer surface
Volume of dispaced water =`pir^(2)h=pi(6)^(2)h=36pih`
Now volume of displaced water =volume of sphere
`36pih=(256pi)/(3)`
`h=(256)/(3xx36)=(64)/(27)cm`
Increase ion height of the water surface =`64//27` cm