Question

Sectio
Q13. Using Euler's formule find the unknown
2
5
2
2
Faces
Vertices
Edges
9​

Answer 1

Step-by-step explanation:

Solution:

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

(i) In the figure we can see that top and bottom faces are pentagons.

Number of faces, F = 7

Number of edges, E =15

Number of vertices, V =10

Let’s verify Euler’s formula,

F + V - E = 7 + 10 - 15

= 17 - 15 = 2

Thus, Euler's formula is verified.

(ii) In the figure we can see that its top is a square pyramid and the bottom is a square prism.

Number of faces, F = 9

Number of edges, E = 16

Number of vertices, V = 9

Let’s verify Euler’s formula,

F + V - E = 9 + 9 - 16

= 18 - 16 = 2

Thus, Euler's formula is verified