How this calculator works
The radii and perpendicular height determine a right circular frustum. Its slant is the hypotenuse of a right triangle whose other leg is the radius difference. The curved surface area depends on the sum of the radii and the slant. Volume includes the cross term Rr because the radius varies linearly with height. The centroid readout assumes a uniform solid, rather than a thin shell, and measures upwards from the larger bottom circle. A zero top radius gives an ordinary cone; equal radii give a cylinder.
Formula
s² = H²+(R-r)²; V = πH(R²+Rr+r²)/3; lateral = π(R+r)s; total = lateral+πR²+πr²; centroid z = H(R²+2Rr+3r²)/[4(R²+Rr+r²)].
Worked example
For R = 5 m, r = 2 m and height 4 m, the slant is 5 m. Volume is 52π m³, curved area is 35π m² and the two circles contribute 29π m², giving total area 64π m². The uniform solid centroid lies 19/13 m above the bottom.
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Frequently asked questions
Does total area include both ends?
Yes. Use the curved lateral area for an open sleeve, or add only the appropriate circle for a one-ended container.
Can the radii be equal?
Yes. The limiting shape is a cylinder and its solid centroid is halfway up.
Does this handle an angled cut?
No. The cut must be parallel to the circular bottom and the axis perpendicular to both planes. An angled cut has different geometry.