Verily Euler’s formula for the following three dimensional figures:

1.	Verily Euler’s formula for the following three dimensional figures:
Answer» (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.

Answer»

(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.

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