Calculations at a vertical halved right circular cone or semicone. This is a cone that is bisected by a plane passing through its apex and the center of its base. In this context, the term lateral surface refers to the curved portion of the surface, specifically, the bisected lateral surface of the circular cone.
Enter radius and height and choose the number of decimal places. Then click Calculate.
Formulas:
pi:
Radius, height and length have the same unit (e.g. meter), surfaces have this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit -1.
The base of the half-cone is a semicircle, while the flat side is an isosceles triangle with a base of 2r and legs of length s. These two surfaces, together with the curved lateral surface, constitute the three faces of the half-cone. Thus, it possesses one more face than the original cone. Accordingly, the surface area of this shape is half that of the cone plus the area of the newly added isosceles triangle. The volume is half the volume of the cone.
A half-cone is simultaneously a conical wedge, or cone segment, with s=r there, and a conical sector with an angle of 180 degrees. In particular, calculating the properties of a conical wedge where s≠r, that is, one divided by a vertical but off-center plane, is significantly more complex than that of a half-cone. The reason for this is that a vertical cross-section passing through the center of the cone yields an isosceles triangle, which presents no mathematical difficulties. Conversely, a vertical cut made away from the center produces a hyperbolic segment, which is mathematically far more challenging to handle.
The half-cone is mirror-symmetrical with respect to a plane. Like the dividing plane of the cone, which generates the half-cone, this plane passes through the cone's apex and through the center of the circle at the base. The plane of symmetry is perpendicular to this dividing plane.