Use Euler’s formula to answer question. A polyhedrons has 20 vertices and 20 faces. How many edges does it have?

Question

Use Euler’s formula to answer question.

A polyhedrons has 20 vertices and 20 faces. How many edges does it have?

Options are
-42
-40
-38
-39

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Liliana 1 week 2021-09-09T14:35:58+00:00 1 Answer 0

Answers ( )

    0
    2021-09-09T14:37:20+00:00

    Answer:  The correct option is (C) 38.

    Step-by-step explanation:  Given that a polyhedron has 20 vertices and 20 faces.

    We are to find the number of edges of the polyhedron using Euler’s formula.

    Euler’s formula :

    For any polyhedron, the number of vertices and faces together is exactly two more than the number of edges.

    Mathematically, V − E + F = 2, where V, E and F represents the number of vertices, number of edges and number of faces of the polyhedron.

    For the given polyhedron, we have

    number of vertices, V = 20,

    number of faces, F = 20

    and

    number of edges, E = ?

    Therefore, from Euler’s formula

    V-E+F=2\\\\\Rightarrow 20-E+20=2\\\\\Rightarrow 40-E=2\\\\\Rightarrow E=40-2\\\\\Rightarrow E=38..

    Thus, the required number of edges of the given polyhedron is 38.

    Option (C) is CORRECT.

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