SOLUTION: A closed right circular cylinder 1 m in diameter and 2 m tall is partially filled with water. When lying horizontally, the depth of the water is two-thirds the diameter. How high w

This problem is similar to the "quarter tank problem" (google it and you will

see some resources, there is a good one on Wolfram Alpha)



We need to figure out the cross-sectional area of the liquid as compared to the circular cross-sectional area of the cylinder.  That ratio will also be the ratio of the volume of liquid to the volume of the cylinder, so to get the height of water, we'll just need to multiply the ratio of areas by the length of the cylinder at the very end.  



With the cylinder on its side, the area of the liquid is:

 





where

     R = radius of circular cross-section

     h = height of liquid

     



Plugging in  R=1/2, h=2/3:    



Which means the water will rise to a level of :



   m  when the cylinder is turned upright.