Advertisements
Advertisements
प्रश्न
Using Euler's formula find the unknown:
| Faces | ? | 5 | 20 |
| Vertices | 6 | ? | 12 |
| Edges | 12 | 9 | ? |
Advertisements
उत्तर
\[\text { We know that the Euler's formula is: F+V = E+2 }\]
1 .\[\text { The number of vertices V is 6 and the number of edges E is 12 }.\]
\[\text { Using Euler's formula: }\]
\[\text { F+6 = 12+2 }\]
\[\text { F+6 = 14 }\]
\[\text { F = 14-6 }\]
\[\text { F = 8 }\]
\[\text { So, the number of faces in this polyhedron is 8 }.\]
2. \[\text { Faces, F = 5 }\]
\[\text { Edges, E = 9}.\]
\[\text { We have to find the number of vertices }.\]
\[\text { Putting these values in Euler's formula: }\]
\[\text { 5+V = 9+2 }\]
\[\text { 5+V = 11 }\]
\[\text { V = 11-5 }\]
\[\text { V = 6 }\]
\[\text { So, the number of vertices in this polyhedron is 6 }.\]
3. \[\text { Number of faces F = 20 }\]
\[\text { Number of vertices V = 12 }\]
\[\text { Using Euler's formula: }\]
\[\text { 20+12 = E+2 }\]
\[\text { 32 = E+2 }\]
\[\text { E+2 = 32 }\]
\[\text { E = 32-2 }\]
\[\text { E = 30 }.\]
\[\text { So, the number of edges in this polyhedron is 30 }.\]
संबंधित प्रश्न
The given Figure are prisms or not?
The given Figure are prisms or not?
If a polyhedron has 10 vertices and 7 faces, find the number of edges in it.
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 |
Dice are cubes with dots or dots on the face. Opposite faces of a die always have a total of seven on them.
In the given below net to make dice (cube), the numbers inserted in the square indicate the number of dots in it.
Insert suitable numbers in the blank so that numbers in opposite faces of the die have a total of seven dots.
The following figure, given below, shows shadows of some 3D object when seen under the lamp of an overhead projector:
Using Euler’s formula, find the unknowns.
| Faces | Vertices | Edges |
| ? | 6 | 14 |
How many vertices does the following solid have?
Cone
How many vertices does the following solid have?
Sphere
Find the number of faces in the given shape:
