Cylindrical Wedge (Ungula) Volume

a right circular cylinder of diameter D sliced by a plane through a DIAMETER of the base, rising to a height H at the far side (the base is a semicircle). The volume is a clean V = (2/3) R^2 H = D^2 H/6, with NO pi in it - the pi of the circular base cancels against the integral of the sloping top. A D = 4 ft, H = 3 ft wedge holds (2/3)(2^2)(3) = 8.00 ft^3 (59.8 gal), which is 2/(3 pi) = 21.2% of the 37.70 ft^3 cylinder that boxes it. Use it for a mitered round pipe or duct end cut, the wedge of liquid in a horizontal cylindrical tank tilted just until the liquid reaches the bottom at one end, a cam, or a bar-stock wedge. This is the through-the-diameter wedge; an off-center chord cut, or a slant that clears the far wall, is separate. A shop and takeoff aid; verify critical dimensions on the work.

V = (2/3) R^2 H = D^2 H/6 for a cylinder cut by a plane through a base diameter (base a semicircle, rise H at the far side); no pi (the base pi cancels the sloping-top integral).

The cylindrical wedge (ungula) volume - standard solid geometry as in Machinery's Handbook (Industrial Press), by name; public domain.

Pure solid geometry, public; the base diameter and the wedge height are user-supplied.

Estimate. AHJ and licensed professional govern.

Field names used by the API: base_diameter_ft, height_ft, volume_ft3, volume_gal

• Wedge volume V = (2/3) R^2 H = D^2 H/6, the through-the-diameter cylindrical ungulasolid geometry (integration)
• Scope base a semicircle (plane through the diameter); an off-center chord cut or a far-wall-clearing slant is separatescope of this tile