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The answer to this riddle may not be obvious, but, it is quite simple…the hopper and lampshade have the same angle! This is shown in the graphic.

As with a lampshade (see “A”), a hopper must be made economically. Consequently, a 60º angle (see “B”) for a conical hopper is most commonly manufactured due to its simplicity, accuracy, and least amount of waste generated during fabrication.

The 60º cone for a silo or bin (see “C”) is derived from a semi-circle (see “D”) with a smaller cut-out for the required outlet; it is then rolled into a cone shape (see “E”). With this, the fabricator can quickly make two identical hoppers at 60º with no scrap other than the outlet cut-outs!

Unfortunately, though the 60º cone is attractive economically to fabricate, it generally will not allow for most powders and bulk solids. As a result, a discharge pattern will occur, often yielding such as arching, ratholing, powder flooding, and segregation.