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प्रश्न
A solid has forty faces and sixty edges. Find the number of vertices of the solid.
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उत्तर
By using Euler’s formula for polyhedron
F + V – E = 2
Given, Faces (F) = 40, Edges (E) = 60
⇒ 40 + V – 60 = 2
⇒ V – 20 = 2
⇒ V = 2 + 20 = 22
Hence, the vertices of the solid are 22.
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संबंधित प्रश्न
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| 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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| Faces | y |
| Vertices | 12 |
| Edges | 18 |
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| Faces | 6 |
| Vertices | q |
| Edges | 12 |
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