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प्रश्न
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
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उत्तर
In the given figure, we have
Faces (F) = 9, Vertices (V) = 9 and Edges (E) = 16
On putting these values in Euler’s formula, we get
F + V – E = 2
⇒ 9 + 9 – 16 = 2
⇒ 18 – 16 = 2
⇒ 2 = 2
Hence, these values satisfies the Euler’s formula. So, it is a polyhedra.
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संबंधित प्रश्न
Using Euler’s formula, find V if E = 30, F = 12.
If a solid shape has 12 faces and 20 vertices, then the number of edges in this solid is ______.
If the sum of number of vertices and faces in a polyhedron is 14, then the number of edges in that shape is ______.
Euler’s formula is true for all three-dimensional shapes.
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
Using Euler’s formula, find the value of unknown x in the following table.
| Faces | 7 |
| Vertices | 10 |
| Edges | x |
Using Euler’s formula, find the value of unknown y in the following table.
| Faces | y |
| Vertices | 12 |
| Edges | 18 |
Using Euler’s formula, find the value of unknown p in the following table.
| Faces | p |
| Vertices | 6 |
| Edges | 12 |
Can a polyhedron have V = F = 9 and E = 16? If yes, draw its figure.
Check whether a polyhedron can have V = 12, E = 6 and F = 8.
