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Question
A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the volume of water
- displaced out of the cylinder
- left in the cylinder.
Solution
We have,
Internal radius of the cylindrical vessel, `"R" = 10/2 = 5 "cm"`
Height of the cylindrical vessel, H = 10.5 cm,
Radius of the solid cone, `r = 7/2 = 3.5 "cm"`
height of the sollid cone, h = 6 cm
(i) Volume of water displaced out of the cylinder = Volume of the solid cone
`= 1/3pi"r"^2"h"`
`= 1/3xx22/7xx3.5xx3.5xx6`
= 77 cm3
(ii) As,
Volume of the cylindrical vessel = πR2H
`= 22/7xx5xx5xx10.5`
= 825 cm3
So, the volume of water left in the cylindrical vessel = Volume of the cylindrical vessel
= 825 - 77
= 748 cm3
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