Hemisphere (3D) — free printable diagram

What a hemisphere is, and how to count it

A hemisphere is a 3D solid that has 1 flat face, 1 edge 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

Hemisphere

Surfaces

1 flat circular face + 1 curved surface

Flat faces

1

Edges

1

Vertices (corners)

0

Is it a polyhedron?

No — it has a curved surface

Volume

V = ⅔πr³

Surface area

SA = 3πr² in total — 2πr² of curved surface plus the πr² flat circle

• A hemisphere is exactly half a sphere, cut through the centre, so its volume is half a sphere's — but its surface area is not half a sphere's, because cutting it open adds a flat circular face that was not there before. That is the step students miss.
• The rim where the flat circle meets the curved surface is usually counted as one edge, and there are no vertices.
• A bowl, a dome and half an orange are all hemispheres.