A cylinder is a three-dimensional geometric figure with two identical and parallel bases connected by a continuous curved surface.

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A red sphere fits perfectly inside a transparent blue cylinder, illustrating Archimedes' relationship between the surface area and volume of a sphere and its circumscribing cylinder, with labeled formulas and dimensions.

The normal, or perpendicular, at each point of a surface defines the corresponding tangent plane, and vice versa.

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3D shapes A group of three-dimensional geometric solids—pyramid, cube, sphere, cone, and cylinder.

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Q: What is a right circular cylinder?

A right circular cylinder has circles for bases, with its axis perpendicular to the plane of the bases. It consists of two parallel, congruent circular bases and a curved lateral surface.

Q: How is the surface area of a right circular cylinder calculated?

Each of the bases of the right circular cylinder has an area of π r 2, where r is the radius of the cylinder. The area of the curved surface connecting the bases is 2π rh , where h is the height of the cylinder. Therefore the total surface area is π r 2+ π r 2+ 2π rh , or 2π r ( r + h ).

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Oct. 5, 2026 •History

What is a cylinder?

What is a right circular cylinder?

How is the surface area of a right circular cylinder calculated?

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°.