Count the number of faces, vertices, and edges of given polyhedra and verify Euler's formula. The maximum value of V+F is:
1.Here,No. of Faces (F):5
No. of Vertices (V):6
No. of Edges (E):9
Euler’s formula: F + V = E + 2
⇒ 5 + 6 = 9 + 2
⇒ 11 = 11
∴ Euler’s formula satisfies for the shape.
2.Here,
No. of Faces (F):7
No. of Vertices (V):10
No. of Edges (E):15
Euler’s formula: F + V = E + 2
⇒ 7 + 10 = 15 + 2
⇒ 17 = 17
∴ Euler’s formula satisfies for the shape.
3.Here,
No. of Faces (F):8
No. of Vertices (V):12
No. of Edges (E):18
Euler’s formula: F + V = E + 2
⇒ 8 + 12 = 18 + 2
⇒ 20 = 20
∴ Euler’s formula satisfies for the shape.
4.Here,
No. of Faces (F):6
No. of Vertices (V):6
No. of Edges (E):10
Euler’s formula: F + V = E + 2
⇒ 6 + 6 = 10 + 2
⇒ 12 = 12
∴ Euler’s formula satisfies for the shape.
5.Here,
No. of Faces (F):5
No. of Vertices (V):5
No. of Edges (E):8
Euler’s formula: F + V = E + 2
⇒ 5 + 5 = 8 + 2
⇒ 10 = 10
∴ Euler’s formula satisfies for the shape.
6.Here,No. of Faces (F):8
No. of Vertices (V):12
No. of Edges (E):18
Euler’s formula: F + V = E + 2
⇒ 8 + 12 = 18 + 2
⇒ 20 = 20
∴ Euler’s formula satisfies for the shape.
7.Here,
No. of Faces (F):8
No. of Vertices (V):6
No. of Edges (E):12
Euler’s formula: F + V = E + 2
⇒ 8 + 6 = 12 + 2
⇒ 14 = 14
∴ Euler’s formula satisfies for the shape.
8.Here,
No. of Faces (F):7
No. of Vertices (V):10
No. of Edges (E):15
Euler’s formula: F + V = E + 2
⇒ 7 + 10 = 15 + 2
⇒ 17 = 17
∴ Euler’s formula satisfies for the shape.
No. of Faces (F):5
No. of Vertices (V):6
No. of Edges (E):9
Euler’s formula: F + V = E + 2
⇒ 5 + 6 = 9 + 2
⇒ 11 = 11
∴ Euler’s formula satisfies for the shape.
2.Here,
No. of Faces (F):7
No. of Vertices (V):10
No. of Edges (E):15
Euler’s formula: F + V = E + 2
⇒ 7 + 10 = 15 + 2
⇒ 17 = 17
∴ Euler’s formula satisfies for the shape.
3.Here,
No. of Faces (F):8
No. of Vertices (V):12
No. of Edges (E):18
Euler’s formula: F + V = E + 2
⇒ 8 + 12 = 18 + 2
⇒ 20 = 20
∴ Euler’s formula satisfies for the shape.
4.Here,
No. of Faces (F):6
No. of Vertices (V):6
No. of Edges (E):10
Euler’s formula: F + V = E + 2
⇒ 6 + 6 = 10 + 2
⇒ 12 = 12
∴ Euler’s formula satisfies for the shape.
5.Here,
No. of Faces (F):5
No. of Vertices (V):5
No. of Edges (E):8
Euler’s formula: F + V = E + 2
⇒ 5 + 5 = 8 + 2
⇒ 10 = 10
∴ Euler’s formula satisfies for the shape.
No. of Faces (F):8
No. of Vertices (V):12
No. of Edges (E):18
Euler’s formula: F + V = E + 2
⇒ 8 + 12 = 18 + 2
⇒ 20 = 20
∴ Euler’s formula satisfies for the shape.
7.Here,
No. of Faces (F):8
No. of Vertices (V):6
No. of Edges (E):12
Euler’s formula: F + V = E + 2
⇒ 8 + 6 = 12 + 2
⇒ 14 = 14
∴ Euler’s formula satisfies for the shape.
8.Here,
No. of Faces (F):7
No. of Vertices (V):10
No. of Edges (E):15
Euler’s formula: F + V = E + 2
⇒ 7 + 10 = 15 + 2
⇒ 17 = 17
∴ Euler’s formula satisfies for the shape.
