Fraction of a Can

Fill a cylindrical can with water.  A quick way to empty the can to exactly half its volume is to pour out the water until the water line just touches the circular bottom of the can.  If you tip the can further, until the water line crosses the center of the bottom of the can (forming a diameter of the bottom circle), what fraction of the can's volume is now filled with water?

Source: Original.

Solutions were receive from Radu Ionescu, Dan Dima, Richard Mathar, Dan Chirica, Nick McGrath, David Bachtel, Kirk Bresniker, Sean Forbes, Alan O'Donnell, Jeremy Galvagni, Yucel Ozcan, Ramneek Sharma, Philippe Fondanaiche, Raśl Mora Pastor.  Many solvers sent the (incorrect) solution of half the volume of a cone: 1/6.  Most then attacked the problem again and found the needed integrals to solve the problem.  I didn't realize that an application of calculus would be required.  Kirk Bresniker found a reference for this problem at  The solution below is from Raśl Mora Pastor.


Mail to Ken