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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
In a solid if F = V = 5, then the number of edges in this shape is ______.
If the sum of number of vertices and faces in a polyhedron is 14, then the number of edges in that shape is ______.
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 x in the following table.
| Faces | 7 |
| Vertices | 10 |
| Edges | x |
Using Euler’s formula, find the value of unknown y in the following table.
| Faces | y |
| Vertices | 12 |
| Edges | 18 |
Using Euler’s formula, find the value of unknown p in the following table.
| Faces | p |
| Vertices | 6 |
| Edges | 12 |
A polyhedron has 60 edges and 40 vertices. Find the number of its faces.
A polyhedron has 20 faces and 12 vertices. Find the edges of the polyhedron.
