semispheres

A semisphere is a geometric shape that represents exactly half of a sphere. Imagine slicing a sphere perfectly through its center; the resulting two halves are semispheres. Each semisphere has a curved surface and a flat circular base, which is the cross-section created by the slicing plane.

The surface area of a semisphere is the sum of the area of its curved surface and the area of its flat base. The curved surface area of a semisphere is half the surface area of the full sphere, which is 2 times pi times the radius squared (2πr²). The flat base is a circle with an area of pi times the radius squared (πr²). Therefore, the total surface area of a semisphere is 3πr².

The volume of a semisphere is precisely half the volume of the full sphere. The volume of a sphere is (4/3)πr³, so the volume of a semisphere is (2/3)πr³. This geometric shape appears in various contexts, from architectural designs to the study of solid geometry. In everyday life, objects like bowls or domes can be approximated as semispheres.