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प्रश्न
Using Euler’s formula, find V if E = 30, F = 12.
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उत्तर
E = 30, F = 12
Euler’s formula:
F + V = E + 2
∴ 12 + V = 30 + 2
∴ 12 + V = 32
∴ V = 32 – 12 = 20
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 |
Which of the following cannot be true for a polyhedron?
If a solid shape has 12 faces and 20 vertices, then the number of edges in this solid is ______.
If the sum of number of vertices and faces in a polyhedron is 14, then the number of edges in that shape is ______.
Euler’s formula is true for all three-dimensional shapes.
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.
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.
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 y in the following table.
| Faces | y |
| Vertices | 12 |
| Edges | 18 |
Using Euler’s formula, find the value of unknown z in the following table.
| Faces | 9 |
| Vertices | z |
| Edges | 16 |
Can a polyhedron have V = F = 9 and E = 16? If yes, draw its figure.
A polyhedron has 60 edges and 40 vertices. Find the number of its faces.
A solid has forty faces and sixty edges. Find the number of vertices of the solid.
