* Hemisphere: This is the most common and general term. It refers to half of a sphere, like the Northern or Southern Hemisphere of Earth.
* Spherical cap: This term is often used in geometry and mathematics, and specifically refers to a portion of a sphere cut off by a plane. A half-sphere is a special case of a spherical cap where the plane passes through the center of the sphere.
* Dome: This term is often used in architecture and engineering, and it typically refers to a curved roof or ceiling resembling a half-sphere.
* Half-sphere: This is a straightforward and descriptive term, though it's less formal than "hemisphere" or "spherical cap."
Ultimately, the best term to use depends on the specific context and the level of formality required.