Question

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

Faces	$9$
Vertices	$z$
Edges	$16$

Answer 1

Step: Finding the value of $z$ .

Number of faces $\left(F\right)=9.$
Number of vertices $\left(V\right)=z$.
Number of edges $\left(E\right)=16.$

Using Euler’s formula for a polyhedron, we have:
$F+V-E=2$
$\Rightarrow 9+z–16=2$
$\Rightarrow z–7=2$
$\therefore z=9$

Therefore, the value of $z$ is $9.$