Question

Find number of faces of a polyhedron, which has 27 edges and 17 vertices.



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Answer 1

Answer:

12

Step-by-step explanation:

In geometry, there is a really nifty, simple and extremely useful thing called Euler's formula, and it looks like this:

V−E+F=2 , where.

V= the number of vertices of a polyhedron.

E= the number of edges of a polyhedron.

F= the number of faces of a polyhedron.

V=17 , E=27 , F=? .

V-E+F=2

17-27+F=2

F=2+27-17

F=12

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Answer 2

Answer :-

• Number of faces = 12

To Find :-

• Number of faces of a polyhedron.

Given :-

• Number of edges = 27

• Number of vertices = 17

Step By Step Explanation :-

In this question we already know the number of edges and number of vertices = 27 and 17 respectively. We need to find the number of faces.

We can find the number of faces using Euler's formula that is ⤵

${\bf{ \red{Faces + Vertices - Edges = 2}}}$

By substituting the values ⤵

$\implies\sf \: Faces + 17 - 27 = 2 \\ \\ \implies\sf Faces - 10 = 2 \\ \\ \implies\sf Faces = 2 + 10 \\ \\ \implies\sf Faces = 12$

Therefore number of faces = 12

Check :-

L. H. S.

=> 12 + 17 - 27

=> 29 - 27

=> 2

R. H. S.

=> 2

Therefore L. H. S. = R. H. S.

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