Can a polyhedron have 10 faces, 20 edges and 15 vertices?

Solution:

According to Euler’s formula in any polyhedron, F + V - E = 2, where ‘F’ stands for a number of faces, ‘V’ stands for a number of vertices and ‘E’ stands for a number of edges.

Given that, 

Number of faces, F = 10

Number of edges, E = 20

Number of vertices, V =15

Let’s verify Euler’s formula,

F + V - E = 10 + 15 - 20

= 25 - 20

= 5 ≠ 2

As we know that according to Euler’s formula in any polyhedron, F + V - E = 2. The above condition doesn't satisfy Euler's formula. Thus, we cannot have a polyhedron with 10 faces, 20 edges and 15 vertices.

☛ Check: NCERT Solutions for Class 8 Maths Chapter 10

Video Solution:

Can a polyhedron have 10 faces, 20 edges and 15 vertices?

Maths NCERT Solutions Class 8 Chapter 10 Exercise 10.3 Question 8

Summary:

No, we cannot have a polyhedron with 10 faces, 20 edges, and 15 vertices as it doesn't satisfy Euler's formula.

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