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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.
Solution
We have,
height of cone, h = 60 cm
the base radius of cone, r =30 cm,
the height of cyllinder, 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.
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