A circular cylinder has two congruent circular bases in parallel planes. Its radius describes a base, and its height is the perpendicular distance between the base planes. Surface area measures its boundary; volume measures the three-dimensional region it encloses.
Right and oblique cylinders: height is the key distinction
In a right cylinder, the generators along the curved side are perpendicular to the bases, so their lengths equal the height. In an oblique cylinder, the generators slant and are longer than that perpendicular height. A right cylinder whose height equals its diameter has a square axial cross-section and is sometimes called an equilateral cylinder.
Rotating a rectangle about one of its sides produces a right circular cylinder. The rotating side fixes its height, while the perpendicular side sweeps the radius. The circular directrix is a curve, not a single point.
Base area, curved area and total surface area
Each base is a disk of radius r. The unrolled curved side of a right cylinder has width equal to the base circumference and height h. Add both bases to that lateral area for a closed cylinder’s total surface. The volume is base area multiplied by perpendicular height.
The base-area and volume formulas also apply to an oblique circular cylinder using perpendicular height. The displayed lateral-area formula assumes a right cylinder. An open container lacks one or both circular covers, so its material area differs from the closed surface.
Worked example: a drum with radius 60 cm and height 110 cm
First square the radius to obtain 3600. Multiplying by π gives one base’s area. For the lateral surface, multiply the circumference by 110. Add two base areas for the total; multiply one base area by 110 for the volume.
The exact values retain π. Since one litre equals 1000 cubic centimetres, dividing the volume coefficient by 1000 gives 396π litres, approximately 1244.07 litres. Square centimetres describe the surface and cannot be used for capacity.
Geometric volume versus usable capacity
These calculations describe an ideal cylinder. For an actual drum, use internal dimensions for capacity and account for wall thickness, rounded ends or unused space when those details matter. Its outside dimensions do not automatically equal the dimensions of the stored liquid. See plane-shape areas for the circular bases and rectangular lateral net.
