cylinder
cylinder, three-dimensional geometric figure that has two identical and parallel bases connected by a continuous curved surface. However, the term cylinder is most often used for what is more strictly speaking the right circular cylinder, which has circles for bases and which has the centers of the circles on an axis perpendicular to the bases. The perpendicular distance between the bases is the cylinder’s height h.
For a right circular cylinder of height h and bases with radius r, the surface area is found by adding up the areas of the two bases and the side surface. Each base has an area of πr2. The area of the curved surfaces is 2πrh, where 2πr is the circumference of the circles that serve as the bases. Therefore, the surface area is πr2+ πr2 + 2πrh = 2πr(r+h)The volume V of the right circular cylinder is V = πr2h.
Cylinders are classified by the shape of their bases and the orientation of the axis relative to the base. The right circular cylinder was discussed above. In the oblique circular cylinder, the axis is not perpendicular to the bases. Although the bases are circular and parallel, the side surface slants at an angle that is not 90°.
A cylinder may also have bases that are not circles. For example, if the bases are ellipses, the shape is an elliptical cylinder.