Question

Q – 4 Find the solution using Euler’s formula. (06) (1) If the number of vertices (V) is 6 and Edges (E) is 12 in a polyhedron, then find its number of Faces(F). (2) Can a polyhedron have 20 Faces, 30 Edges and 12 Vertices? Prove by Euler’s formula.​

Answer 1

$\huge{\textbf{\textsf{{\color{navy}{Ans}}{\purple{we}}{\pink{r}} {\color{pink}{:}}}}}$

Explanation:

Faces-?,vertices-6,edges-12

Euler's formula: F+V–E=2

F+6–12=2

F=2+12–6=8

F=8

(ii) Faces-5,vertices-?,edges-9

Euler's formula: F+V–E=2

5+V–9=2

V=2+9–5=6

V= 6

(iii) Faces-20,vertices-12,edges-?

Euler's formula: F+v–E=2

20+12–E=2 ,

E=20+12–2

E=30

Answer 2

Answer:

Euler's polyhedron formula, V−E+F=2

V = number of vertices = 6

E = number of edges = 12

F = number of faces = ?

6−12+F=2

F=6+2

F=8

Number of faces = 8

A octahederon has8 faces and 6 vertices with 12 edges.

Explanation:

$\huge \pink{Queen \:Medusa}$