Question

A conical vessel whose internal radius is 10 cm and height 48 cm is full of water. Find the volume of water. If this water is poured into a cylindrical vessel with internal radius 20 cm, find the height to which the water level rises in it.

Answer 1

Radius of conical vessel r = 10 cm

Height of conical vessel h = 48 cm

The volume of water = volume of conical vessel.

`=1/3 pir^2 h`

`= 1/3pi  xx 100 xx 48`

` = 1600pi  cm^3`

`1600 xx 3.14`

` = 5024 cm^3`

Let h' be the height of cylindrical vessel, which filled by the water of conical vessel,

Radius of cylindrical vessel = 20 cm

Clearly,

Volume of cylindrical vessel = volume of water

`pi xx (20)^2 xx h = 1600 pi`

                      ` h =(1600)/400`

                      ` h = 4  cm`

Thus, the volume of the cylindrical vessel and height of cylindrical vessel are  `5024  cm^3` and 4cm respectively.