Question

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

Faces	$p$
Vertices	$6$
Edges	$12$

Answer 1

Step: Finding the value of $p$ .

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

Using Euler’s formula for a polyhedron, we have:
$F+V-E=2$
$\Rightarrow p+6–12=2$
$\Rightarrow p–6=2$
$\therefore p=8$
Therefore, the value of $p$ is $8.$