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प्रश्न
If the sum of number of vertices and faces in a polyhedron is 14, then the number of edges in that shape is ______.
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उत्तर
If the sum of number of vertices and faces in a polyhedron is 14, then the number of edges in that shape is 12.
Explanation:
Given, the sum of number of vertices and faces in a polyhedron is 14, i.e. V + F = 14
We know that, Euler’s formula, F + V – E = 2 for any polyhedron.
⇒ 14 – E = 2
⇒ 14 – 2 = E
⇒ E = 12
Hence, the number of edges are 12.
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संबंधित प्रश्न
Using Euler's formula, find the values of x, y, z.
| Faces | Vertices | Edges | |
| (i) | x | 15 | 20 |
| (ii) | 6 | y | 8 |
| (iii) | 14 | 26 | z |
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Using Euler’s formula, find the value of unknown y in the following table.
| Faces | y |
| Vertices | 12 |
| Edges | 18 |
Can a polyhedron have V = F = 9 and E = 16? If yes, draw its figure.
