The solid cut from a horizontal cylinder of length and radius by a single plane oriented parallel to the cylinder's axis of symmetry (i.e., a portion of a horizontal cylindrical tank which is partially filled with fluid) is called a horizontal cylindrical segment.

For a cut made a height above the bottom of the horizontal cylinder (as illustrated above), the volume of the cylindrical segment is given by multiplying the area of a circular segment of height by the length of the tank ,

plotted above. Note that the above equation gives , , and , as expected. Since a circular segment is the cross section of the horizontal cylindrical segment, determining the fraction of the tank that is full is equivalent to determining the fractional area of a circle covered by the circular segment.

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 is sometimes known as the quarter-tank problem.

More things to try:

Weisstein, Eric W. "Horizontal Cylindrical Segment." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HorizontalCylindricalSegment.html