Calculations at a right truncated elliptic cone. This is an elliptic cone with the tip cut off. Enter the two semi axes lengths at the base and the height of cone and truncated cone. Choose the number of decimal places, then click Calculate. The lateral surface is calculated with an integral and can only be estimated here.
Formulas:
j = h - i
c = a * j / h
d = b * j / h
L ≈ 1/2 * π * [ ( a * √ b² + h² + b * √ a² + h² ) - ( c * √ d² + j² + d * √ c² + j² ) ]
A = L + π * ( a * b + c * d )
V = π / 3 * ( h * a * b - j * c * d )
pi:
π = 3.141592653589793...
Semi axes and heights have the same unit (e.g. meter), the surfaces have this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter).
The lateral surface is the curved part of the surface area. This cannot be calculated algebraically but only estimated. This estimate is more accurate the taller the truncated cone and the more circular the ellipses are. For a right truncated circular cone, a simple calculation is possible. As with the truncated circular cone, the truncated tip of an elliptical truncated cone is also called a supplementary cone. In this case, it is a similar, smaller elliptical truncated cone.
If you look at a truncated cone from the side, the two-dimensional outline is a trapezoid. When looking perpendicularly at the semi-axes, it is an isosceles trapezoid.
The truncated elliptical cone has the same symmetry properties as the elliptical cone. It is therefore mirror-symmetric about two planes. These are the two planes along the two major and two minor semi-axes of the elliptical base and the ellipse of the truncated apex, respectively. It is also rotationally symmetric at an angle of 180 degrees and multiples thereof. The axis of rotation passes through the centers of both ellipses.
