Spherical Zone (Segment of Two Bases) Volume

By the prismatoid rule V = (pi h/6)(3 r1^2 + 3 r2^2 + h^2) from the two circular face radii r1, r2 and the height h between them, needing no parent-sphere radius. A zone with r1 = 4 ft, r2 = 3 ft, h = 2 ft holds 82.7 ft^3 (619 gal). Use it for the liquid between two levels in a spherical tank (the incremental volume from one dipstick to the next), a spherical band, or a dome zone. One base zero collapses to the spherical cap. The lateral zone surface 2 pi R h (needs the sphere radius), and an ellipsoidal or off-axis zone, are separate. A takeoff aid; verify against the tank chart or drawing.

V = (pi h/6)(3 r1^2 + 3 r2^2 + h^2), r1/r2 the two circular face radii and h the perpendicular distance between the planes (prismatoid rule); one base zero gives the spherical cap.

The spherical zone (segment of two bases) volume by the prismatoid rule - standard solid geometry as in Machinery's Handbook (Industrial Press), by name; public domain.

Pure solid geometry, public; the two face radii and the zone height are user-supplied.

Estimate. AHJ and licensed professional govern.

Field names used by the API: base_radius_1_ft, base_radius_2_ft, zone_height_ft, volume_ft3, volume_gal

• Zone volume V = (pi h/6)(3 r1^2 + 3 r2^2 + h^2), the prismatoid rule (no sphere radius needed)solid geometry
• Scope one base zero is the spherical cap; the lateral surface and an off-axis/ellipsoidal zone are separatescope of this tile