A closed cylindrical tank is 9ft. long and 4ft. in diameter, when lying in horizontal position, the water is 3ft. deep. if the tank is in vertical position, what is the depth of the water in the tank?

Question

mathmate · Answer

This problem can be solved by integrating the volume of a circular section of radius 1 from -1 to 1/2, i.e. 3/4 full.  The proportion of this area related to the area of the section is then the ratio of the height of water to the height of the cylinder.
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