halbkugelige

Halbkugelige, or hemispherical, describes a shape formed by one half of a sphere cut by a plane that passes through the sphere’s center. The solid consists of a curved, dome-like surface and a flat circular base with radius r.

Geometrically, a hemispherical solid has volume V = (2/3)πr^3. Its curved surface area is A_curved = 2πr^2, and if the base is included, the total surface area is A_total = 3πr^2. The centroid of a solid hemisphere lies on its axis of symmetry at a distance of 3r/8 from the flat base.

There are variations of halbkugelige. A hollow hemispherical shell has mass distributed over the curved surface with area 2πr^2 (excluding the base, unless it is present). A hemispherical dome or cap is a surface subset of a sphere bounded by a plane through the center, often used in architecture, design, and optics.

Applications range from architectural domes and decorative elements to optical components such as hemispherical lenses or mirrors, where the shape helps manage wavefronts and focal properties. In science and engineering, hemispherical geometries are used to study symmetry, pressure distribution, and acoustic or thermal behavior in dome-like structures.

In related terms, the concept contrasts with a full sphere, a spherical cap, or a hemispherical shell, highlighting the half-sphere’s distinctive combination of curved surface and flat base.