Right Cylinder Volume
A right cylinder is the standard cylinder shape — two parallel circular bases connected by a curved surface that is perpendicular to both bases. No tilt, no slant. This is the shape of most cans, glasses, and pipes. V = πr²h gives the volume directly.
Right Cylinder Volume
What Makes a Cylinder 'Right'
A right cylinder has its axis perpendicular to its bases. The line connecting the centers of the two circular bases forms a 90° angle with each base. This is the default cylinder shape in geometry.
The word 'right' distinguishes it from an oblique cylinder, which is tilted so the axis is not perpendicular to the bases. Both have the same volume formula, but the 'right' version is simpler to visualize and measure.
Every cross-section parallel to the base is an identical circle, and every cross-section perpendicular to the base is a rectangle.
Properties of a Right Cylinder
Volume: V = πr²h Lateral surface area: 2πrh Total surface area: 2πr(r + h) Base area: πr²
The axis length equals the height. The slant height also equals the height (since there's no tilt). Every point on the curved surface is the same distance (r) from the axis.
A right cylinder is also called a 'right circular cylinder' because its bases are circles. If the bases were ellipses, it would be a right elliptical cylinder.
Right Cylinder vs Other Cylinder Types
Right circular cylinder: Upright, circular bases, perpendicular sides. The most common type.
Oblique cylinder: Tilted. Same base but the sides lean. Same volume as a right cylinder with the same base and perpendicular height.
Hollow cylinder: Has an inner cavity. Volume = πh(R² − r²).
Elliptical cylinder: Bases are ellipses, not circles. V = π × a × b × h.
For most practical purposes — cans, tanks, glasses, pipes — you're working with a right circular cylinder.