A polyhedron can have 10 faces, 20 edges and 15 vertices. State whether the statement is true or false.

Solution:

Given, A polyhedron can have 10 faces, 20 edges and 15 vertices.

We have to determine if the given statement is true or false

Euler’s formula for any polyhedron is given by

F + V – E = 2

Where F stands for number of faces,

V for number of vertices

E for number of edges.

Given, F = 10

V = 15

E = 20

Now, F + V – E = 10 + 15 - 20

= 25 - 20

= 5

Therefore, a polyhedron cannot have 10 faces, 20 edges and 15 vertices.

✦ Try This: A polyhedron can have 12 faces, 10 edges and 8 vertices. State whether the statement is true or false.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 10

NCERT Exemplar Class 8 Maths Chapter 6 Problem 49

A polyhedron can have 10 faces, 20 edges and 15 vertices. State whether the statement is true or false.

Summary:

The given statement, ”A polyhedron can have 10 faces, 20 edges and 15 vertices” is false.

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