Question

Verify Euler's formula for the following three dimentional 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.