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प्रश्न
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
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उत्तर
In the given figure, we have
Faces (F) = 11, Vertices (V) = 11 and Edges (E) = 20
On putting these values in Euler’s formula, we get
F + V – E = 2
⇒ 11 + 11 – 20 = 2
⇒ 22 – 20 = 2
⇒ 2 = 2
Hence, these values satisfies the Euler’s formula. So, it is a polyhedra.
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संबंधित प्रश्न
Using Euler's formula, find the values of x, y, z.
| Faces | Vertices | Edges | |
| (i) | x | 15 | 20 |
| (ii) | 6 | y | 8 |
| (iii) | 14 | 26 | z |
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.
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 q in the following table.
| Faces | 6 |
| Vertices | q |
| Edges | 12 |
Can a polyhedron have V = F = 9 and E = 16? If yes, draw its figure.
A polyhedron has 20 faces and 12 vertices. Find the edges of the polyhedron.
