Question

A solid right circular cone of height 60 cm and radius 30 cm is dropped in a right circular cylinder full of water, of height 180 cm and radius 60 cm. Find the volume of water left in the cylinder, in cubic metres.

Answer 1

We have,

Height of cone, h = 60 cm

The base radius of cone, r = 30 cm,

The height of cylinder, H = 180 cm and 

The base radius of the cylinder, R = 60 cm

Now,

Volume of water left in the cylinder, = Volume of cylinder - Volume of cone

`= piR^2H-1/3pir^2h`

`= 22/7xx60xx60xx180-1/3xx22/7xx30xx30xx60`

`= 22/7xx30xx30xx60(2xx2xx3-1/3)`

`= 22/7xx54000(12-1/3)`

`=22/7xx54000xx35/3`

`= 1980000  "cm"^3`

`= 1980000/1000000 "m"^3`

`=1.98  "m"^3`

So, the volume of water left in the cylinder is 1.98 m³.