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7.Using Euler’s formula find the unknown.


Answer :

In the first case we have: Vertices =6, Edges =12
By Euler’s formula, F + V= E + 2

F= 12 + 2-6 =8

Hence, faces =8

In 2nd case we have : Faces = 5, Edges = 9

By Euler’s formula, F + V = E + 2

V = E + 2 – F = 9+ 2- 5 = 6

Hence, vertices =6

In 3rd case we have : Faces =20, Vertices =12

By Euler’s formula, we know that F+V=E+2

E = F + V – 2 = 20 + 12 – 2 = 30

Hence, edges =30