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प्रश्न
A polyhedron has 60 edges and 40 vertices. Find the number of its faces.
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उत्तर
By using Euler’s formula for polyhedron,
F + V – E = 2 ...[Where, F = faces, V = vertices, E = edges]
⇒ F + 40 – 60 = 2 ...[∵ E = 60 and V = 40, given]
⇒ F – 20 = 2
⇒ F = 2 + 20
⇒ F = 22
Hence, the number of faces are 22.
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संबंधित प्रश्न
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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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