# 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.

**☛ Related Questions:**

- Can a polyhedron have for its faces (i) 3 triangles? (ii) 4 triangles? (iii) a square and four triangles?
- Is it possible to have a polyhedron with any given number of faces? (Hint: Think of a pyramid).
- Which are prisms among the following?(i) How are prisms and cylinders alike? (ii) How are pyramids and cones alike?
- (i) How are prisms and cylinders alike? (ii) How are pyramids and cones alike?

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