Cylinder (3D) — free printable diagram

What a cylinder is, and how to count it

A cylinder is a 3D solid that has 2 flat faces, 2 edges and 0 vertices. Part of its surface is curved, so it is not a polyhedron and it is counted differently from a cube or a prism — which is also why Euler's formula does not apply to it.

Solid

Cylinder

Surfaces

2 flat circular faces + 1 curved surface

Flat faces

2

Edges

2

Vertices (corners)

0

Is it a polyhedron?

No — it has a curved surface

Volume

V = πr²h

Surface area

SA = 2πr² + 2πrh

• The volume formula is the prism rule in disguise: area of the end × length, where the end happens to be a circle.
• How many faces a cylinder has depends on the wording your syllabus uses. Some count 3, treating the curved surface as a face; others say 2 flat faces and 1 curved surface. Check which your curriculum expects before marking it.
• Unrolled, the curved surface is a rectangle whose width is the circumference of the circle, 2πr — which is where the 2πrh term comes from.
• A tin of beans and a drinks can are cylinders.