Tapered (Frustum) Tank Volume from Level

The partial liquid volume of a straight-TAPERED (frustum) tank or bin from a dipstick depth - a tapered silo, a hopper, or a process tank whose diameter changes top to bottom, the shape frustum-volume gives only when full. The radius grows linearly with height, r(h) = R1 + (R2 - R1) h/H, so the liquid up to depth h is itself a frustum: V = (pi h/3)(R1^2 + R1 r(h) + r(h)^2). A tank tapering from 4 ft at the bottom to 10 ft at the top over 12 ft holds 3,666 gallons full but only 1,093 (29.8%) at the 6 ft mark, because a widening tank fills fastest near the top - the gauge is non-linear. It handles a widening bin or a narrowing hopper; equal diameters collapse to a straight cylinder. Enter inside dimensions in feet. A right frustum with flat top and bottom; a bottom cone under a cylinder is a separate shape. Reported in cubic feet and US gallons with the percent full.

r(h) = R1 + (R2 - R1) h/H; volume = (pi h/3)(R1^2 + R1 r(h) + r(h)^2); full = (pi H/3)(R1^2 + R1 R2 + R2^2).

Tapered (frustum) tank partial gauging - the liquid up to a level is itself a cone frustum; standard solid geometry (frustum of a cone) as in Machinery's Handbook (Industrial Press), by name; public domain.

Public-domain solid geometry; the bottom and top diameters, the height, and the depth are user-supplied.

Estimate. AHJ and licensed professional govern.

Field names used by the API: bottom_diameter_ft, top_diameter_ft, height_ft, depth_ft, volume_gal, percent_full

• Partial volume V = (pi h/3)(R1^2 + R1 r(h) + r(h)^2), a frustum up to the level with r(h) linearsolid geometry
• Scope right frustum, flat top/bottom; equal diameters give a cylinder; a cone-under-cylinder is the cone-bottom tilescope of this tile