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Using Euler’s formula find the unknown
Using Euler’s formula find the unknown

Solution:

According to Euler’s formula, in any polyhedron, F + V - E = 2, where ‘F’ stands for the number of faces, ‘V’ stands for the number of vertices and ‘E’ stands for the number of edges.

(i) Number of faces, F =?

Number of edges, E =12

Number of vertices, V = 6

According to Euler’s formula in any polyhedron,

F + V - E = 2

F + 6 - 12 = 2

F - 6 = 2

F = 2 + 6 = 8

(ii) Number of faces, F = 5

Number of edges, E = 9

Number of vertices, V = ?

According to Euler’s formula in any polyhedron,

F + V - E = 2

5 + V - 9 = 2

V - 4 = 2

V = 2 + 4 = 6

(iii) Number of faces, F = 20

Number of edges, E = ?

Number of vertices, V = 12

According to Euler’s formula in any polyhedron,

F + V - E = 2

20 + 12 - E = 2

32 - E = 2

E = 32 - 2 = 30

Faces 8 5 20
Vertices 6 6 12
Edges 12 9 30

☛ Check: NCERT Solutions for Class 8 Maths Chapter 10

Video Solution:

Using Euler’s formula find the unknown

Maths NCERT Solutions Class 8 Chapter 10 Exercise 10.3 Question 7

Summary:

Using Euler’s formula the unknowns are (i) The value of F is 8 (ii) The value of V is 6 (iii) The value of E is 30

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