document.write( "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? \n" ); document.write( "
Algebra.Com's Answer #388641 by Theo(13342)\"\" \"About 
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The volume of the cube is equal to s^3.
\n" ); document.write( "s = 5.5
\n" ); document.write( "V = (5.5)^3
\n" ); document.write( "The volume of the cylinder is equal to pi*r^2*h
\n" ); document.write( "diameter is equal to 11.
\n" ); document.write( "radius is equal to half that.
\n" ); document.write( "r = 5.5
\n" ); document.write( "The volume of the water is the same volume as the cube.
\n" ); document.write( "The only difference is the shape of the container.
\n" ); document.write( "This means that the volume of the cube has to be equal to the volume of the water.
\n" ); document.write( "The volume of the cube is equal to (5.5)^3 which is equal to 166.375 cm^3 (cubic centimeters).
\n" ); document.write( "The volume of the cylinder is equal to pi*r^2*h and that volume must be equal to 166.375 cm^3.
\n" ); document.write( "The equation for the cylinder is therefore 166.375 = pi*r^2*h.
\n" ); document.write( "since the radius of the cylinder is equal to 5.5 cm, the formula for the cylinder becomes:
\n" ); document.write( "166.375 = pi*(5.5)^2*h
\n" ); document.write( "we can take this formula and solve for h to get:
\n" ); document.write( "h = 166.375 / (pi*(5.5)^2)
\n" ); document.write( "The result of that gets you:
\n" ); document.write( "h = 1.750704373
\n" ); document.write( "dropping the cube into the cylinder of water will make the water rise by 1.750704373 cm^3.
\n" ); document.write( "That's due to the equivalent volume of water that has been displaced.\r
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