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There is some water in a cylindrical ves...

There is some water in a cylindrical vessel of diameter `11 cm` . A solid cube of side `5.5 cm` is dropped into the water , which immersed completely in the water . Find the increase in the height of surface of water in the vessel.

A

`1.25 cm`

B

`1.5 cm`

C

`1.75 cm`

D

`2.00 cm`

Text Solution

Verified by Experts

The correct Answer is:
C
Volume of cube `=("side")^(3)=(5.5)^(3)cm^(3)`
Diameter of vessel `(2 r) = 11 cm`
`rArr r = (11)/(2)=5.5 cm`
Let the surface of water increases `= h cm`
`therefore` Volume of displace water `= pi r^(2)h = (22)/(7)xx(5.5)^(2)xxh`
Now, volume of displaced water = volume of cube
`rArr (22)/(7)xx(5.5)^(2)xxh=(5.5)^(3)`
`rArr h=(5.5xx7)/(22)=1.75`
`therefore` The increase in the surface of water = `1.75 cm.`
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