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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) = 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
Verify Euler’s formula for the following three-dimensional figures:
A polyhedron can have 10 faces, 20 edges and 15 vertices.
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 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.
A solid has forty faces and sixty edges. Find the number of vertices of the solid.
