Question

A hemispherical bowl of internal radius 9 cm is full of water. Its contents are emptied into a cylindrical vessel of internal radius 6 cm. Find the height of water in the cylindrical vessel.

Answer 1

We have,

the radius of the hemispherical bowl, R=9 cm and 

the internal base radius of the cylindrical vessel, be h.

As,

Volume of water in the cylindrical vessel=Volume of hemispherical bowl

`rArr pir^2h = 2/3piR^3`

`rArr r^2h = 2/3 R^3`

`rArr 6xx6xxh=2/3xx9xx9xx9`

`rArr "h" =2/3 xx (9xx9xx9)/(6xx6)`

`rArr "h" = 27/2`

`rArr "h" =27/2`

∴ h=13.5 cm

so,the height of the water in the cylindrical vessel is 13.5 cm.