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The numbers of vertices (V), edges (E) and faces (F) of a polyhedron are respectively 10, 15 and x. Then, the value of (3x-12) is:
Question

The numbers of vertices (V), edges (E) and faces (F) of a polyhedron are respectively 10, 15 and x.
Then, the value of (3x-12) is:

A.

9

B.

14

C.

18

D.

7

Correct option is A

By the Euler's relation for polyhedra, We know that
F+V=E+2
Given mumber of edges = 15
Number of vertices = 10
the number of faces = x
Now putting these values in the Euler's relation, we get
F+V=E+2
x+10=15+2
x=15+2−10
x=7
3x-12 = 3×7-12=9

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