What Is a Cylinder?

The measurements that define it

Cylinder volume is found the same way prism volume is found: base area multiplied by perpendicular height. That connection helps students see cylinders as part of a wider family of solids with repeated cross sections.

This page keeps the bases, radius, axis, and height visible together so the cylinder can be read as a precise solid and not only as the shape of a can.

If a cylinder has radius 3 units and height 10 units, its volume is the area of one circular base, 9π, multiplied by 10, giving 90π cubic units. The curved side does not change the base area; it carries that same circle through the height.

A cylinder is a prism-like solid with a circular base. That comparison is useful because it explains why the volume formula is base area times height, while the curved surface requires circumference times height when it is unwrapped.

• A cylinder has two congruent circular bases connected by a curved surface.
• The height of a cylinder is the perpendicular distance between the two bases.
• If the side surface is unrolled in a right cylinder, it forms a rectangle.
• A cylinder has no edges in the polyhedron sense because its side surface is curved.

Where cylinders help

• Use cylinders in volume and surface-area problems involving tanks, cans, pipes, and rollers.
• Use them when comparing curved solids with prisms and cones.
• Use cylinder cross sections to study how slicing direction changes the resulting shape.

Cylinder checks to make

• Do not use a slanted side length in place of perpendicular height.
• Do not forget that the base radius belongs to the circles at the ends, not to the full height.
• Do not treat the curved surface as if it were made of polygon faces.