halvkule

Halvkule, or hemisphere, is the solid formed by dividing a sphere into two equal parts with a plane that passes through the sphere’s center. Each half is a halvkule. The term is used both for the solid half and for its curved surface, depending on context.

Geometrically, a halvkule of radius r has a curved surface area of 2πr^2. If the flat circular base is included, the total surface area is 3πr^2. The volume of a halvkule is (2/3)πr^3, and the base has area πr^2. The half-sphere is congruent to its sister half, created by the same central plane.

A halvkule is obtained by cutting a sphere with a plane that passes through the center; two halvkuler together reconstruct the original sphere. The symmetry axis runs from the center of the sphere to the center of the base.

Centroid and density: For a solid halvkule with uniform density, the center of mass lies on the symmetry axis at a distance of 3r/8 from the flat base toward the curved surface.

Etymology and usage: The name originates from halv- (half) and kule/kugle (sphere or ball) in Scandinavian languages. Halvkuler are common in mathematics and physics, and the shape appears in architecture, mechanisms, and models as a simple round form such as domes, bowls, or half-ball components.