Question

Use Euler's formula to find the value of $a,b$ and $c$

	Faces	Vertices	Edges
(i)	8	a	12
(ii)	b	6	9
(iii)	20	12	c

Answer 1

We know that, $Eulerformula=F+V=E+2$

$\Rightarrow F+V-E=2$

$\left(i\right)F=8,V=a,E=12$

So, by formula, we get:

$\begin{array}{c}8+a-12=2\\ a-4=2\\ \Rightarrow a=6\end{array}$

$\left(ii\right)F=b,v=6,E=9$

So, by formula, we get:

$\begin{array}{c}b+6-9=2\\ b-3=2\\ \Rightarrow b=5\end{array}$

$\left(iii\right)F=20,v=12,E=c$

So, by formula, we get:

$\begin{array}{c}20+12-c=2\\ 32-c=2\\ 32-2=c\\ \Rightarrow c=30\end{array}$

Hence, $a=6,b=5$ and $c=30$.