Calculations at a bicone or double cone. This is a right circular cone with an identical cone attached to its base the other way around.
Enter radius or diameter of the base and half height or height and choose the number of decimal places. Then click Calculate. The half height is the height of the original cone, the surface area is twice the original lateral surface and the volume is twice that of the cone.
Formulas:
d = 2 * r
H = 2 * h
A = 2 * r * √ h² + r² * π
V = 2/3 * r² * π * h
pi:
π = 3.141592653589793...
Radius, diameter and heights have the same unit (e.g. meter), the surface area has 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 intersection of the bicone from vertex to vertex is a rhombus. The bicone is mirror-symmetrical to the plane through the central circle, which is also the base of the two individual cones. It is also point-symmetrical to the center of this circle. Furthermore, it is rotationally symmetrical to the axis through the two vertices for any angle. The bicone is therefore a solid of revolution.
A truncated bicone is formed in a similar way to a bicone. Other cones, such as an elliptic cone or an oblique circular cone, can also be made into bicones, which then have twice the volume and twice the surface area minus the two base areas. Oblique circular cones can be duplicated axially symmetrically, in which case both vertices point in the same direction, or doubled point symmetrically, in which case both vertices point in opposite directions. A general cone normally cannot be duplicated in this way. Instead of two identical shapes, you need a mirror shape, a shape that is mirrored at its base, and then fitted together with the previous shape.