FACES EDGES AND VERTICES WORKSHEET

Question 1 :

In a 3-D shape, what are faces, edges and vertices?

Question 2-6 : Name and write the number of faces (F), vertices (V) and edges (E) for the following polyhedrons. Also find F + V – E.

Question 2 :

Question 3 :

Question 4 :

Question 5 :

Question 6 :

Question 7 :

What do you observe from the answers of the above questions 2 to 6?

1. Answer :

A cube. A cube is made of six square shaped planes. These 6 square shaped planes of the cube are known as its faces.

A line segment which connects any two faces of a cube is called as Edge and each corner point where three edges meet is called as Vertex. So, a cube has 6 faces, 12 edges and 8 vertices.

2. Answer :

Name : Cube

Face : 6

Vertices : 8

Edges : 12

F + V - E = 6 + 8 - 12 = 2

3. Answer :

Name : Cuboid

Face : 6

Vertices : 8

Edges : 12

F + V - E = 6 + 8 - 12 = 2

4. Answer :

Name : Triangular Prism

Face : 5

Vertices : 6

Edges : 9

F + V - E = 5 + 6 - 9 = 2

5. Answer :

Name : Square Pyramid

Face : 5

Vertices : 5

Edges : 8

F + V - E = 5 + 5 - 8 = 2

6. Answer :

Name : Triangular Pyramid

Face : 4

Vertices : 4

Edges : 6

F + V - E = 4 + 4 - 6 = 2

7. Answer :

We observe that, F + V – E = 2 in all the cases.

This is true for any polyhedron and this relation

F + V – E = 2

is known as Euler’s formula.

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