Quarter-Tank Problem


Finding the height above the bottom of a horizontal cylinder (such as a cylindrical gas tank) to which the it must be filled for it to be one quarter full amounts to plugging A=piR^2/4 (one quarter of the area of a full circle) into the equation for the area of a circular segment of radius R,


This gives equality between the two shaded areas in the above figure, resulting in


where x=h/R and R is the radius of the circle or cylinder. This cannot be solved analytically, but the solution can be found numerically to be approximately x=0.596027... (OEIS A133742), corresponding to h=0.596027R.

See also

Circular Segment, Cylinder, Cylindrical Segment, Horizontal Cylindrical Segment

Explore with Wolfram|Alpha


Sloane, N. J. A. Sequence A133742 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Quarter-Tank Problem

Cite this as:

Weisstein, Eric W. "Quarter-Tank Problem." From MathWorld--A Wolfram Web Resource.

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