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प्रश्न
A polyhedron can have 10 faces, 20 edges and 15 vertices.
पर्याय
True
False
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उत्तर
This statement is False.
Explanation:
We know that, Euler’s formula satisfies for every polyhedron.
i.e. F + V – E = 2
Here, F = 10, E = 20
And V = 15
On putting these values in the Euler’s formula, we get
10 + 15 – 20 = 2
⇒ 25 – 20 = 2
⇒ 5 ≠ 2
Hence, the given values does not satisfy the Euler’s formula.
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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 |
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 x in the following table.
| Faces | 7 |
| Vertices | 10 |
| Edges | x |
Can a polyhedron have V = F = 9 and E = 16? If yes, draw its figure.
A polyhedron has 60 edges and 40 vertices. Find the number of its faces.
A solid has forty faces and sixty edges. Find the number of vertices of the solid.
