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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
Using Euler’s formula, find V if E = 30, F = 12.
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 ______.
Which of the following cannot be true for a polyhedron?
If a solid shape has 12 faces and 20 vertices, then the number of edges in this solid is ______.
If the sum of number of vertices and faces in a polyhedron is 14, then the number of edges in that shape is ______.
A polyhedron can have 10 faces, 20 edges and 15 vertices.
Complete the table given below:
| S.No | Solid | Shape of Solid |
Number of faces F |
Number of Verticles V |
Number of edges E |
F + V | E + 2 |
| a. | Cuboid |  |
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| b. | Triangular Pyramid |
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| c. | Square Pyramid |
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| d. | Rectangular Pyramid |
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| e. | Pentagonal Pyramid |
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| f. | Hexagonal Pyramid |
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| g. | Triangular Prism |
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| h. | Square Prism |
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| i. | Cube |  |
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| j. | Pentagonal Prism |
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| k. | Octagonal Prism |
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| l. | Heptagonal Prism |
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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 |
