Question

if a solid has 5 faces and 9 edges , by Euler's formula the number of vertices is ?

Answer 1

Number of faces; F = 5
Number of edges; E = 9
Number of Vertices = V
So according to the euler's formula, number of vertices is given by;
$$\begin{gathered} \mathrm{V}-\mathrm{E}+\mathrm{F}=2 \\ \Rightarrow \mathrm{V}-9+5=2 \\ \Rightarrow \mathrm{V}-4=2 \\ \Rightarrow \mathrm{V}=2+4=6 \end{gathered}$$
Therefore number of vertices is 6.