Advertisements
Advertisements
प्रश्न
Can a polyhedron have 10 faces, 20 edges and 15 vertices?
Advertisements
उत्तर
\[\text { No, because every polyhedron satisfies Euler's formula, given below: }\]
\[\text { F+V=E+2 }\]
\[\text { Here, number of faces F = 10 }\]
\[\text { Number of edges E = 20 }\]
\[\text { Number of vertices V = 15 }\]
\[\text { So, by Euler's formula: }\]
\[\text { LHS: 10+15 = 25 }\]
\[\text { RHS: 20 + 2 = 22 }, \]
\[\text { which is not true because 25 }\neq22\]
\[\text { Hence, Eulers formula is not satisfied and no polyhedron may be formed .}\]
संबंधित प्रश्न
The given Figure are prisms or not?
Using Euler’s formula, find the unknown.
| Faces | ? | 5 | 20 |
| Vertices | 6 | ? | 12 |
| Edges | 12 | 9 | ? |
Using Euler's formula find the unknown:
| Faces | ? | 5 | 20 |
| Vertices | 6 | ? | 12 |
| Edges | 12 | 9 | ? |
If a polyhedron has 10 vertices and 7 faces, find the number of edges in it.
State, the number of faces, number of vertices and number of edges of:
(i) a pentagonal pyramid
(ii) a hexagonal prism
The figure, given below, shows shadows of some 3D object when seen under the lamp of an overhead projector:
A triangle
In this case, name the object.
Using Euler’s formula, find the values of a, b, c and d.
| Faces | a | 5 | 20 | 6 |
| Vertices | 6 | b | 12 | d |
| Edges | 12 | 9 | c | 12 |
The following figure represent the nets of some solid. Name the solid
How many vertices does the following solid have?
Cylinder
How many vertices does the following solid have?
Octagonal Pyramid
