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प्रश्न
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
उत्तर
In the given figure, we have
Faces (F) = 5, Vertices (V) = 6 and Edges (E) = 9
On putting these values in Euler's formula, we get
F + V – E = 2
⇒ 5 + 6 – 9 = 2
⇒ 11 – 9 = 2
⇒ 2 = 2
Hence, these values satisfies the Euler's formula. So, it is a polyhedra.
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संबंधित प्रश्न
Which of the following cannot be true for a polyhedron?
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 x in the following table.
| Faces | 7 |
| Vertices | 10 |
| Edges | x |
Using Euler’s formula, find the value of unknown z in the following table.
| Faces | 9 |
| Vertices | z |
| Edges | 16 |
Using Euler’s formula, find the value of unknown q in the following table.
| Faces | 6 |
| Vertices | q |
| Edges | 12 |
Using Euler’s formula, find the value of unknown r in the following table.
| Faces | 8 |
| Vertices | 11 |
| Edges | r |
A polyhedron has 60 edges and 40 vertices. Find the number of its faces.
