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प्रश्न
Check whether a polyhedron can have V = 12, E = 6 and F = 8.
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उत्तर
By using Euler’s formula for polyhedron,
F + V – E = 2 ...[Where, F = faces, V = vertices, E = edges]
⇒ 8 + 12 – 6 = 2
⇒ 20 – 6 = 2
⇒ 14 ≠ 2
∴ Given values do not satisfy the Euler’s formula. It mean this type of polyhedron cannot be possible.
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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 |
Which of the following cannot be true for a polyhedron?
Euler’s formula is true for all three-dimensional shapes.
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.
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.
Can a polyhedron have V = F = 9 and E = 16? If yes, draw its figure.
