Cone (3D Shape) — free printable clipart

What a cone is, and how to count it

A cone is a 3D solid that has 1 flat face, 1 edge and 1 vertex. 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

Cone

Surfaces

1 flat circular base + 1 curved surface

Flat faces

1

Edges

1

Vertices (corners)

1

Is it a polyhedron?

No — it has a curved surface

Volume

V = ⅓πr²h

Surface area

SA = πr² + πrl, where l is the slant height

• The volume is exactly one third of the cylinder that would fit snugly around it — same radius, same height. Pouring rice from a cone into a cylinder is the standard way to show it.
• The vertical height h and the slant height l are two different measurements. Volume needs h, curved surface area needs l, and they are linked by Pythagoras: l² = r² + h².
• The single point at the top is called the apex. It is usually counted as the cone's one vertex.
• As with a cylinder, whether the curved surface counts as a “face” depends on the curriculum's wording, so a cone is variously described as having 1 or 2 faces.