Three-Dimensional 3D Shapes

Solid figures are three-dimensional 3D objects. What this means is solid shapes have width, depth, and height.

Basic Properties of some Solid 3D Figures

Faces, Edges, and Vertices of Solids:

(i) Face: A face is a flat surface. Faces can be square, rectangular or circular

(ii) Edge: The edge of a solid figure is the line segment where two faces meet.

(iii) Vertex: The corners where the edges meet are called vertices.

1) Cuboid:

Properties of Cuboid:

• A cuboid has 6 faces. 

• A cuboid has 12 edges.

• A cuboid has 8 Vertices.

• It has rectangular faces.

Examples

Shoebox, cereal box, jewellery box

2) Cube

Properties of a Cube:

• A cube has 6 faces.

• All the faces of a cube are square in shape

• A cube has 12 edges.

• All the 12 edges are equal in length because all faces are squares

• A cube has 8 Vertices.

Example: dice, maggi, Rubik’s cube

3) Cylinder:

Properties of a Cylinder:

• Circular cross-section.

• Two circular bases – one at its base and another at its top.

• It has two edges, at which the two plane (flat) surfaces meet with the curved surface. These edges are curved edges.

• A cylinder has 3 faces – The two plane surfaces and the curved surface.

• There are no vertices.

Example: coke can, glass cup, pipe.

4) Cone

Properties of Cone

• It has a circular base 

• A cone has 1 Vertex

• A cone has 2 faces.

• A cone has 1 Edge

Example: Birthday cap, ice-cream cone.

5) Sphere

Properties of Sphere:

• Each point on a sphere is at an equal distance from the centre.

• In a sphere, there are no faces, edges, or vertices.

Examples: soccer ball, tennis ball, earth.

5) Pyramid:

A pyramid is named according to the shape of its base.

Examples are:

1. Triangular-based pyramid (tetrahedron) 
2. Rectangular-based pyramid
3. Square-based pyramid
4. Hexagonal-based pyramid.

Properties of Triangular-based Pyramid (Tetrahedron) 

• It has 4 faces.

• The 3 side faces are triangles. The base is also a triangle which adds up to 4 faces in total

• It has 4 vertices (corner points).

• It has 6 edges & also a tetrahedron.

Properties of Square-based Pyramid:

• It has 5 faces.

• The 4 side faces are triangles. The base is a square, which adds up to 5 faces in total

• It has 5 vertices (corner points).

• It has 8 edges.

Relationship between the numbers of Faces (F) Vertices (V) and Edges (E)

This chart gives you an idea of some of the faces, edges of vertices of common solid figures.

Solid	No of Vertices	No of Faces	No of Edges
Cuboid	8	6	12
Cube	8	6	12
Sphere	0	0	0
Triangular based Prism	6	5	9
Cone	1	2	1
Triangular based Pyramid	4	4	6
Square-based Pyramid	5	5	8
Hexagonal-based pyramid	7	7	12
Cylinder	0	3	2