Question

Verify Euler’s formula for the following three-dimensional figures:

Answer 1

(i) 

Number of vertices = 6
Number of faces = 8
Number of edges = 12
Using Euler formula,
F + V – E = 2
8 + 6 – 12 = 2
2 = 2 Hence proved.

(ii) 

Number of vertices = 9
Number of faces = 8
Number of edges = 15
Using, Euler’s formula,
F + V – E = 2
9 + 8 – 15 = 2
2 = 2 Hence proved.

(iii) 

Number of vertices = 9
Number of faces = 5
Number of edges = 12
Using, Euler’s formula,
F + V – E = 2
9 + 5 – 12 = 2
2 = 2 Hence proved.