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# 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 (one quarter of the area of a full circle) into the equation for the area of a circular segment of radius ,

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

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

Circular Segment, Cylinder, Cylindrical Segment, Horizontal Cylindrical Segment

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## References

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. https://mathworld.wolfram.com/Quarter-TankProblem.html