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Truncated Cone Volume Calculator

Compute volume and lateral area of a truncated cone: V = (π·h/3)·(R²+r²+R·r). For containers and construction.

Volume of a frustum of a cone

A frustum (truncated cone) is a cone with its top cut off by a plane parallel to the base. The volume is V = (πh/3)·(R² + r² + R·r), where R is the larger radius, r the smaller and h the height between the two circular faces. It generalises to any frustum as V = (h/3)·(A₁ + A₂ + √(A₁·A₂)). Example: R = 10 cm, r = 5 cm, h = 12 cm → V = (12π/3)·(100 + 25 + 50) = 700π ≈ 2,199 cm³. When r = 0 the formula collapses to the regular cone (πR²h/3).

Applications

Buckets, conical cups, lampshades, paint cans, margarine tubs and many supermarket packages have a frustum shape. Used in engineering for cooling towers of power plants, hoppers and silos, and in marketing for calculating product volume in non-cylindrical packaging.

FAQ

What if r = 0? It becomes a regular cone with volume V = πR²h/3.

And if R = r? The result is a cylinder, V = πR²h.

Does the formula work in litres? Yes — use cm for the dimensions and divide cm³ by 1,000 to get litres.

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