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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) = 3, Vertices (V) = 0 and Edges (E) = 2
On putting these values in Euler’s formula, we get
F + V – E = 2
⇒ 3 + 0 – 2 = 2
⇒ 1 ≠ 2
Hence, these values do not satisfy the Euler’s formula. So, it is not 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 |
Which of the following cannot be true for a polyhedron?
Euler’s formula is true for all three-dimensional shapes.
A polyhedron can have 10 faces, 20 edges and 15 vertices.
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 p in the following table.
| Faces | p |
| Vertices | 6 |
| Edges | 12 |
Check whether a polyhedron can have V = 12, E = 6 and F = 8.
A polyhedron has 20 faces and 12 vertices. Find the edges of the polyhedron.
