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प्रश्न
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
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
Verify Euler’s formula for the following three-dimensional figures:
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 |
If a solid shape has 12 faces and 20 vertices, then the number of edges in this solid is ______.
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
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 r in the following table.
| Faces | 8 |
| Vertices | 11 |
| Edges | r |
Can a polyhedron have V = F = 9 and E = 16? If yes, draw its figure.
