hemispherical

Hemispherical is an adjective describing something that resembles or relates to a hemisphere, the half of a sphere produced by a plane that passes through the sphere’s center. The term can refer to either the curved surface of such a half or the solid half that includes the flat circular base.

In geometry, a hemisphere is formed by dividing a sphere with a plane through its center. The curved surface area of a hollow hemisphere is 2πr^2, where r is the radius. The total surface area of a solid hemisphere (including the base) is 3πr^2. The solid hemisphere contains half the volume of a full sphere, equal to (2/3)πr^3. The hemisphere is a special case of a spherical cap, representing the half of the sphere bounded by the cutting plane.

Hemispherical shapes are common in design and technology. Architectural domes and shells often use hemispherical forms for structural efficiency and aesthetic effect. In optics and acoustics, hemispherical lenses, reflectors, and domes influence how light or sound is collected and distributed. In communications and sensing, hemispherical antennas and hemispherical camera fields of view exploit the half-sphere geometry to cover broad directions. In anatomy, the term also appears in reference to the cerebral hemispheres, the two halves of the brain, which together coordinate function and perception.