Question

Find whether the following table satisfies the EULER'S formula or not. [4 MARKS]

$\begin{array}{ccc}\text{No. of Faces}& \text{No. of Vertices}& \text{No. of Edges}\\ 3& 4& 6\\ 3& 8& 12\\ 4& 6& 12\\ 3& 20& 30\\ 5& 12& 30\end{array}$

Answer 1

Formula: 1.5 Marks
Application: 0.5 Mark each

Euler’s Formula:
Faces + Vertices – Edges = 2

1) 3 + 4 - 6 = 1

1 $\ne$ 2


2) 3 + 8 -12 = -1

1 $\ne$ 2


3) 4 + 6 - 12 = -2

-2 $\ne$ 2


4) 3 + 20 - 30 = -7

-7 $\ne$ 2


5) 5 + 12 - 30 = -13

-13 $\ne$ 2