semicylinder

A semicylinder is the half of a right circular cylinder obtained by slicing the cylinder with a plane that contains its axis. The two halves are congruent, so each semicylinder represents one half of the original cylinder. In many contexts, a semicylinder can refer to the solid half, including its curved surface, the flat cut face, and the two semicircular end faces, or to the curved surface alone, which is called a semicylindrical surface.

For a semicylinder with radius r and height h (the length along the cylinder’s axis), the volume is half the volume of the full cylinder. Thus, V = (1/2) π r^2 h. The surface area depends on what is counted as a boundary. The curved surface is half of the full cylinder’s curved area, giving a curved surface area of π r h. The cut along the axial plane forms a rectangular face of dimensions 2r by h, with area 2 r h. Each end face is a semicircle of radius r, giving a combined area of π r^2 for the two ends. Therefore, the total surface area of the solid semicylinder is S = π r h + 2 r h + π r^2.

Variations exist: if only the curved semicylindrical surface is considered, its area is π r h; if the shape is described as a surface rather than a solid, the end faces and the cut plane may be excluded. Semicylinders appear in architecture, ducts, and other engineering contexts where a half-round cross-section is needed.

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