Question

⏺verify Euler's formula for the given figure⏺

Answer 1

In 1st figure
Faces =6
Edges=12
Vertices =8
Verification :F + V= E + 2
=>6 + 8 =12 + 2
=>14 = 14. verified

In 2nd figure
Faces = 9
Edges = 16
Vertices=9
Verification :F + V = E + 2
=>9+9=16+2
=>18 = 18. verified

hope it helps

Answer 2

Concept

Euler’s formula is F + V - E = 2 in any polyhedron, where 'F' represents the number of faces, 'V' represents the number of vertices, and 'E' represents the number of edges.

Given

Figures

(i)

(ii)

To find

For the given figure we have to verify  Euler's formula.

Solution

(i)

The top and bottom faces are quadrilateral in the figure.

Number of faces, F = 6

Number of edges, E = 12

Number of vertices, V = 8

Let’s verify Euler’s formula,

F + V - E = 6 + 8 - 12

= 14 - 12 = 2

Thus, Euler's formula is verified.

(ii)

The top of the figure is a square pyramid, while the bottom is a square prism.

Number of faces, F = 6

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.