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
Draw net for the following polyhedron :
Match the following figure:
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.
The following figure represent the nets of some solid. Name the solid
Verify Euler’s formula for the table given below.
| Faces | Vertices | Edges |
| 32 | 60 | 90 |
How many faces does the following solid have?
Tetrahedron
How many vertices does the following solid have?
Tetrahedron
How many edges does the following solid have?
Sphere
The corners of solid shapes are called its ______.
How many faces does a cylinder have?
