Silo + Hopper Capacity (3D)

What this calculator is

Textbook physics/chemistry, SI-friendly. The Silo + Hopper Capacity (3D) on MyCalcsWorld is for homework checks and first-cut estimates under idealized assumptions unless noted. What it does: Cylinder bin plus conical hopper capacity and lateral area — with interactive 3D silo. Typical inputs: Cylinder radius (m), Cylinder height (m), Hopper height (m), Hopper outlet radius (m). People often land here searching for silo, hopper, grain bin, cone, 3d. Demo defaults (cylinder radius 2 m, cylinder height 8 m, hopper height 3 m, hopper outlet radius 0.2 m) currently resolve to Total capacity 114.4796 in the live panel — change any field to explore sensitivity. Who it helps: lab students, makers, and engineers doing first-cut checks with textbook identities before applying real tolerances. Nearby tools people often open next: cone frustum 3d, tank fill 3d, pyramid volume 3d. Below the live form you get MyCalcsWorld-specific guidance — when to use this Silo + Hopper Capacity (3D), common mistakes, how to interpret results, step-by-step how-to, a worked example with real numbers, formula notes, and FAQs. Charts and tables appear in the results panel whenever this engine provides them. Science & Engineering related tools are linked so you can jump without starting from search.

When to use / who it helps

• Grain or pellet bin volume.
• Comparing hopper angles via height/outlet.
• Teaching cylinder + cone volume.
• Use the Silo + Hopper Capacity (3D) for homework checks and first-cut design estimates under textbook assumptions.
• Keep SI (or the form’s stated units) consistent — a wrong unit ruins precision.

How to interpret results

• Total capacity is geometric volume.
• Convert to mass with bulk density separately.
• Outlet radius 0 is a pointed cone.
• On the Silo + Hopper Capacity (3D), read the large primary result first, then secondary totals, then any chart or table.
• Each result is driven only by the labeled inputs (Cylinder radius (m), Cylinder height (m), Hopper height (m), Hopper outlet radius (m)); anything not on the form (fees, holidays, clinical adjustments) is outside this estimate.

Common mistakes & gotchas

• Using diameter as radius.
• Ignoring packing density for mass.
• Assuming perfect cone discharge.
• Mixing SI and customary units across: Cylinder radius (m), Cylinder height (m), Hopper height (m), Hopper outlet radius (m).
• Ignoring that textbook models omit friction, temperature drift, or non-ohmic behavior.

How to calculate / formula

Cylinder V = πR²Hc. Hopper frustum V = πHh(R²+Rr+r²)/3. Science tools apply textbook relationships (Ohm’s law, density, kinematics, waves, energy) with SI units unless the form asks otherwise. Idealized assumptions (constant g, ohmic resistors, frictionless motion) apply unless noted — real lab or field conditions need your own corrections. For the Silo + Hopper Capacity (3D), the labeled fields (Cylinder radius (m), Cylinder height (m), Hopper height (m), Hopper outlet radius (m)) drive the live result panel.

Frequently asked questions