Page 265 - Start Up Mathematics_7

Faces, Edges and Vertices
We have already learnt about faces, edges and vertices of solid shapes. Let’s find them for the
following solids.

Cube:

(i) Vertices: The 8 corners of a cube are its vertices.
Vertices

(ii) Edges: A cube has 12 edges as shown in the adjoining
figure. Edges

(iii) Faces: The 6 flat surfaces that form a cube are called its
faces. Face

Now let’s find the vertices, edges and faces of a pyramid and a cone.

Pyramid: Cone: Vertex
A triangular pyramid as shown has: A cone has:

(i) 4 vertices Vertex (i) one vertex Curved
surface
(ii) 6 edges (ii) one curved edge

(iii) 4 faces Edge (iii) one curved surface
Face
and one flat face Flat face Curved edge

We can clearly see that the faces of 3-D objects are 2-D figures. For example, a cube has six faces
which are squares. A triangular pyramid has triangles as its faces. A cone has a circle as its face.

• The solids which are bounded by polygons as their faces are called polyhedrons.
• If, F, E and V represent the faces, edges and vertices of a polyhedron (prism or pyramid) respectively then
F + V – E = 2. This is known as Euler’s formula.

EXERCISE 15.1

1. Give two examples of objects having shape similar to a:
(a) cylinder (b) cone (c) cube (d) sphere
2. Match the following:
(a) An unsharpened pencil (i) sphere
(b) A table tennis ball (ii) cuboid
(c) A match box (iii) cone
(d) A die (iv) cube
(e) A clown’s cap (v) cylinder

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