halfspherical

Halfspherical, also commonly referred to as hemispherical, describes anything that is half of a sphere. In geometry, a half-sphere is produced by cutting a sphere with a plane through the sphere’s center, yielding two congruent parts. When the solid is considered, the term hemisphere is used; for the curved surface alone, the term hemispherical surface or shell may apply.

Key properties for a hemisphere of radius r: the volume is (2/3)πr^3; the curved surface area is 2πr^2; the flat circular base has area πr^2, and the total surface area of the solid (curved surface plus base) is 3πr^2. The relationship to a full sphere is the hemisphere occupies half the volume of a sphere, with a radius identical to that sphere.

The term halffspherical is a descriptive variant, but hemispherical is generally preferred in technical writing. A halff sphere may also refer to a spherical cap when the cutting plane is not through the center, in which case the shape is not a true hemisphere.

Applications and examples include architectural domes and bowls, hemispherical mirrors and reflectors in optics, radar and satellite antenna covers, and certain 3D-printed or manufactured components that require a half-sphere geometry. In natural and biological contexts, hemispherical shapes appear in objects such as eyeballs and some plant or animal structures, reflecting the prevalence of half-sphere forms in design and function.

See also: hemisphere, spherical cap, sphere.