SOLUTION: a cylinderical vessel of diameter 11cm is filled up with some water.when a cubical solid of side 5.5 cm is immersed in water completely then how much the level of the water will in

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Question 617927: a cylinderical vessel of diameter 11cm is filled up with some water.when a cubical solid of side 5.5 cm is immersed in water completely then how much the level of the water will increase?
Answer by Theo(13342) (Show Source):
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The volume of the cube is equal to s^3.
s = 5.5
V = (5.5)^3
The volume of the cylinder is equal to pi*r^2*h
diameter is equal to 11.
radius is equal to half that.
r = 5.5
The volume of the water is the same volume as the cube.
The only difference is the shape of the container.
This means that the volume of the cube has to be equal to the volume of the water.
The volume of the cube is equal to (5.5)^3 which is equal to 166.375 cm^3 (cubic centimeters).
The volume of the cylinder is equal to pi*r^2*h and that volume must be equal to 166.375 cm^3.
The equation for the cylinder is therefore 166.375 = pi*r^2*h.
since the radius of the cylinder is equal to 5.5 cm, the formula for the cylinder becomes:
166.375 = pi*(5.5)^2*h
we can take this formula and solve for h to get:
h = 166.375 / (pi*(5.5)^2)
The result of that gets you:
h = 1.750704373
dropping the cube into the cylinder of water will make the water rise by 1.750704373 cm^3.
That's due to the equivalent volume of water that has been displaced.