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प्रश्न
If the sum of number of vertices and faces in a polyhedron is 14, then the number of edges in that shape is ______.
उत्तर
If the sum of number of vertices and faces in a polyhedron is 14, then the number of edges in that shape is 12.
Explanation:
Given, the sum of number of vertices and faces in a polyhedron is 14, i.e. V + F = 14
We know that, Euler's formula, F + V – E = 2 for any polyhedron.
⇒ 14 – E = 2
⇒ 14 – 2 = E
⇒ E = 12
Hence, the number of edges are 12.
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संबंधित प्रश्न
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.
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.
Using Euler’s formula, find the value of unknown p in the following table.
| Faces | p |
| Vertices | 6 |
| Edges | 12 |
Using Euler’s formula, find the value of unknown r in the following table.
| Faces | 8 |
| Vertices | 11 |
| Edges | r |
Can a polyhedron have V = F = 9 and E = 16? If yes, draw its figure.
A solid has forty faces and sixty edges. Find the number of vertices of the solid.
