Semisphere

Semisphere is a term used to denote half of a sphere. In geometry, a semisphere is formed when a sphere is cut by a plane that passes through the sphere’s center, producing two congruent halves. Each semisphere can be considered as either a solid region, bounded by the plane and the spherical surface, or as the curved surface alone.

For a semisphere with radius r, the volume of the solid half is (2/3)πr^3. The curved surface area of the hemispherical shell is 2πr^2; if the base circular face (the flat disk where the cut occurred) is included, the total surface area becomes 3πr^2.

In practice, the term semisphere is less common than hemisphere. The standard mathematical term for half a sphere is hemisphere, and semisphere may appear in older texts or in certain contexts. When used, semisphere can refer to either the solid half or the curved surface, with the intended meaning clarified by context.

Etymology and usage: semisphere derives from semi- meaning half and sphaera meaning sphere; in English, hemisphere is the prevailing term, while semisphere is a less frequent variant. The concept remains fundamental to problems involving halves of spheres and their geometric properties.