Detailed definition
Understanding Cylinder
A cylinder has two congruent parallel circular bases connected by a curved lateral surface. In a right cylinder the axis is perpendicular to the bases; in an oblique cylinder it is not.
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.
Key facts
Important ideas to remember
- 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 it is used
Where cylinder shows up
- 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.
Common mistakes
What to watch out for
- 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.