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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) = 6, Vertices (V) = 8 and Edges (E) = 12
On putting these values in Euler’s formula, we get
F + V – E = 2
⇒ 6 + 8 – 12 = 2
⇒ 14 – 12 = 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 the sum of number of vertices and faces in a polyhedron is 14, then the number of edges in that shape 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.
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.
A solid has forty faces and sixty edges. Find the number of vertices of the solid.
