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A cylindrical vessel has a base-radius of 10 cm. It contains water to a depth of 12 cm. A metal pipe whose inner and outer radii
are 4 cm and 6 cm respectively rests vertically on the base of the vessel. Let h the final height of the water level as in the picture,
make an equation and find h. Hence, find the rise in the water level.
I really don't get what the question is asking for!
If they give us the height/depth at the beginning, isn't it the same at the end? What rise???
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When you submerge a solid body into the liquid in the vessel, the body displaces liquid and makes its level higher.
This phenomenon is known for thousands years, and one of famous Archimedes achievement was to find the density of the king's crown
made of unknown material by submerging it into water.
OK. Now let us return to our problem.
This time we have cylindrical hollow tube placed into water in the vessel vertically.
The initial level of the water in the vessel was h = 12 cm.
Then the liquid volume in the vessel is V = .
Let "H" be the raised level of the water in the vessel after the tube submerging.
The area of the space occupied by water is .
I distracted from the area of the tube cross section.
The volume of water remains unchangeable. It gives you an equation
= .
It is your equation to determine H. Solve it for H:
H = .
Now substitute values (and cancel ):
H = = = = = = 15 cm.
Answer. The raised water level after the tume submerging vertically is 15 cm.
Solved. Congrats !!!