semicylinders

A semicylinder is half of a right circular cylinder obtained by cutting the cylinder with a plane that contains the cylinder's axis. The resulting solid has a flat rectangular face along the cut, a curved lateral surface that is a semicylinder, and two end faces that are semicircles.

If the original cylinder has radius r and height h, its volume is half the cylinder’s volume: V = (1/2) π r^2 h. The surface area consists of three parts: the curved semicylindrical surface with area π r h, the two end faces which together form a full circle of area π r^2, and the rectangular cut face with area 2 r h. Therefore the total surface area is A = π r h + π r^2 + 2 r h = r h (π + 2) + π r^2.

The cross-section of a semicylinder is a semicircle of radius r, and the length of the shape equals h. Semicylinders appear in various applications, including architectural elements and manufacturing components where a combination of curved and flat surfaces is desirable. Variations can arise from cutting planes that produce different end shapes, but the term semicylinder typically refers to the half obtained by a plane through the axis of the original cylinder.