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# 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

**☛ Related Questions:**

- Can a polyhedron have for its faces (i) 3 triangles? (ii) 4 triangles? (iii) a square and four triangles?
- Is it possible to have a polyhedron with any given number of faces? (Hint: Think of a pyramid).
- Which are prisms among the following?(i) How are prisms and cylinders alike? (ii) How are pyramids and cones alike?
- (i) How are prisms and cylinders alike? (ii) How are pyramids and cones alike?

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