Truncated Pyramid (Rectangular Frustum) Volume

The volume of a truncated pyramid - a tapered concrete pier or spread-footing pedestal, a rectangular hopper or bin, or a round-to-rectangular transition. Prismatoid formula V = (h/3)(A1 + A2 + sqrt(A1 A2)), A1 = bottom area, A2 = top area. A 6x6 base, 2x2 top, 4 ft pier takes 69.3 ft^3 = 2.57 yd^3 of concrete; averaging the footprints (a 4x4 mean, 64 ft^3) would short the pour by 5 ft^3, because the sqrt(A1 A2) middle term is what makes it exact. Top 0x0 gives a full pyramid (A1 h/3), equal top/bottom a prism (A1 h). Reported in ft^3, yd^3, and gallons. An offset pyramid, wall thickness, and surface area are separate. A takeoff aid; verify against the drawing.

A1 = Lb x Wb; A2 = Lt x Wt; V = (h/3)(A1 + A2 + sqrt(A1 A2)). Top 0x0 -> full pyramid (A1 h/3); equal top/bottom -> prism (A1 h).

The truncated-pyramid volume V = (h/3)(A1 + A2 + sqrt(A1 A2)) - the prismatoid formula, standard solid geometry as in Machinery's Handbook (Industrial Press), by name; public domain.

Pure solid geometry, public; the bottom and top dimensions and the height are user-supplied.

Estimate. AHJ and licensed professional govern.

Field names used by the API: bottom_length_ft, bottom_width_ft, top_length_ft, top_width_ft, height_ft, volume_ft3, volume_yd3

• Prismatoid formula V = (h/3)(A1 + A2 + sqrt(A1 A2)); the sqrt term makes it exactsolid geometry
• Limits top 0x0 gives a full pyramid, equal top/bottom a prismsolid geometry
• Scope right rectangular frustum; round frustum is separate, as are oblique pyramidsscope of this tile