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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
Verify Euler’s formula for the following three-dimensional figures:
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 ______.
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 x in the following table.
| Faces | 7 |
| Vertices | 10 |
| Edges | x |
Check whether a polyhedron can have V = 12, E = 6 and F = 8.
