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प्रश्न
Can a polyhedron have V = F = 9 and E = 16? If yes, draw its figure.
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उत्तर
Given, Vertices = 9, Faces = 9 and Edges = 16
Using Euler’s formula for polyhedron,
F + V – E = 2 ...[Where, F = faces, V = vertices and E = edges]
⇒ 9 + 9 – 16 = 2
⇒ 18 – 16 = 2
⇒ 2 = 2
Hence, the given values satisfies the Euler’s formula.
So, a polyhedron can have V = F = 9 and E = 16
Thus, we can draw a octagonal pyramid.
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संबंधित प्रश्न
Verify Euler’s formula for the following three-dimensional figures:
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 z in the following table.
| Faces | 9 |
| Vertices | z |
| Edges | 16 |
Using Euler’s formula, find the value of unknown q in the following table.
| Faces | 6 |
| Vertices | q |
| Edges | 12 |
Check whether a polyhedron can have V = 12, E = 6 and F = 8.
