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प्रश्न
Using Euler’s formula, find the value of unknown y in the following table.
| Faces | y |
| Vertices | 12 |
| Edges | 18 |
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उत्तर
By using Euler’s formula for polyhedron
From, V = 12, E = 18 and F = y
So, F + V – E = 2
⇒ y + 12 – 18 = 2
⇒ y – 6 = 2
⇒ y = 2 + 6
⇒ y = 8
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संबंधित प्रश्न
Using Euler’s formula, find V if E = 30, F = 12.
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.
A polyhedron has 60 edges and 40 vertices. Find the number of its faces.
