Question

Verify Euler's formula for the given solid.

Answer 1

Lets observe the given solid figure,

In this figure,

Number of Vertices $\left(V\right)=6$ [ $A,B,C,D,E\text{and}F$]

Number of faces $\left(F\right)=8$ [$ABF,AFD,ADE,ABE,CBF,CFD,CDE\text{and}CBE$]

Number of edges $\left(E\right)=12$ [$AB,BF,AF,FD,DA,DE,AE,BE,BC,CD,CE,\text{and}CF$]

According to Euler's formula,
$V-E+F=2$
L.H.S. $=V-E+F$

$=8-12+8$

$=2$

$=$ RHS
Therefore, L.H.S. = R.H.S.
Hence, Euler’s formula is verified.