Cylindrical Wedge (Ungula) Volume Calculator

Find the volume of a cylindrical wedge (ungula) cut from a right circular cylinder by a slanted plane through a base diameter, from the radius and height. Base, curved, and cut areas are shown too.

Input

Enter the radius and height to compute the volume of a cylindrical wedge, the solid cut from a right circular cylinder by a slanted plane through the base diameter.

Radius r

Height h

Result

Volume

133.333333

Radius r

Height h

Half base area

39.269908

Curved surface area

Cut face area

37.047157

The volume is V = (2/3) r^2 h. The half base area is (pi r^2) / 2 and the curved surface area is 2 r h.

Lengths use the same unit as the input, areas are squared, and volume is cubed.

How it works

A cylindrical wedge, or ungula, is the solid left when a right circular cylinder is cut by a slanted plane passing through a diameter of the base.
The plane is assumed to pass through the base diameter and rise to height h at the opposite edge.
The volume is V = (2/3) r^2 h, where r is the base radius and h is the height of the highest point.
The half base area is (pi r^2) / 2 and the curved side surface area is 2 r h.
Lengths use the same unit as the input, areas are squared, and volume is cubed.

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