Question

Using Euler’s formula, Find the value of unknown $q$ in the following table.

Faces	$6$
Vertices	$q$
Edges	$12$

Answer 1

Step: Finding the value of $q$ .

Number of faces $\left(F\right)=6.$
Number of vertices $\left(V\right)=q.$
Number of edges $\left(E\right)=12.$

Using Euler’s formula for a polyhedron, we have:
$F+V-E=2$
$\Rightarrow 6+q–12=2$
$\Rightarrow q–6=2$
$\therefore q=8$

Therefore, the value of $q$ is $8.$