Maths 2 Mark Question

In the given polyhedron: Edges E = 21 Faces F = 9 Vertices V = 14
Now, putting these values in Euler's formula: LHS: F + V = 9 + 14 = 23 RHS: E + 2 = 21 + 2 = 23 This is true. Hence, Euler's formula is satisfied.

In the given polyhedron: Edges E = 8 Faces F = 5 Vertices V = 5
Now, putting these values in Euler's formula: LHS: F + V = 5 + 5 = 10 RHS: E + 2 = 8 + 2 = 10 This is true. Hence, Euler's formula is satisfied.

Among the given figures, only figure (i) is a dice.
This is because if we fold the given net from the edges, we'll get a cube in which the sum of the opposite faces is 7.

2.  

Yes, it is possible to have a polyhedron with any number of faces.
The only condition is that there should be at least four faces.
This is because there is no possible polyhedron with 3 or less faces.

In the given polyhedron: Edges E = 16 Faces F = 9 Vertices V = 9
Now, putting these values in Euler's formula: LHS: F + V = 9 + 9 = 18 RHS: E + 2 = 16 + 2 = 18 This is true. Hence, Euler's formula is satisfied.

In the given polyhedron: Edges E = 16 Faces F = 9 Vertices V = 9
Now, putting these values in Euler's formula: LHS: F + V = 9 + 9 = 18 RHS: E + 2 = 16 + 2 = 18 This is true. Hence, Euler's formula is satisfied.

The least number of planes that can enclose a solid is 4.
Tetrahedron is a solid with four planes (faces).

In the given polyhedron:
Edges E = 15
Faces F = 7
Vertices V = 10

Now, putting these values in Euler's formula:
LHS: F + V = 7 + 10 = 17
LHS: E + 2 = 15 + 2 = 17
LHS = RHS
Hence, the Euler's formula is satisfied.