Page No 167:
Question 7:
Using Euler’s formula, find the unknown.
Faces | ? | 5 | 20 |
Vertices | 6 | ? | 12 |
Edges | 12 | 9 | ? |
By Euler’s formula, we have
F + V − E = 2
(i) F + 6 − 12 = 2
F − 6 = 2
F = 8
(ii) 5 + V − 9 = 2
V − 4 = 2
V = 6
(iii) 20 + 12 − E = 2
32 − E = 2
E = 30
Thus, the table can be completed as
Faces | 8 | 5 | 20 |
Vertices | 6 | 6 | 12 |
Edges | 12 | 9 | 30 |
