Question

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

Faces	$8$
Vertices	$11$
Edges	$r$

Answer 1

Step: Finding the value of $r$ .

Number of faces $\left(F\right)=8.$
Number of vertices $\left(V\right)=11.$
Number of edges =$\left(E\right)=r.$

Using Euler’s formula for a polyhedron, we have:
$F+V-E=2$
$\Rightarrow 8+11–r=2$
$\Rightarrow 19-r=2$
$\therefore r=17$

Therefore, the value of $r$ is $17.$