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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
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 |
In a solid if F = V = 5, then the number of edges in this shape is ______.
If a solid shape has 12 faces and 20 vertices, then the number of edges in this solid 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 q in the following table.
| Faces | 6 |
| Vertices | q |
| Edges | 12 |
Using Euler’s formula, find the value of unknown r in the following table.
| Faces | 8 |
| Vertices | 11 |
| Edges | r |
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.
