Advertisements
Advertisements
प्रश्न
A polyhedron has 60 edges and 40 vertices. Find the number of its faces.
उत्तर
By using Euler's formula for polyhedron,
F + V – E = 2 ...[Where, F = faces, V = vertices, E = edges]
⇒ F + 40 – 60 = 2 ...[∵ E = 60 and V = 40, given]
⇒ F – 20 = 2
⇒ F = 2 + 20
⇒ F = 22
Hence, the number of faces are 22.
APPEARS IN
संबंधित प्रश्न
Verify Euler’s formula for the following three-dimensional figures:
In a solid if F = V = 5, then the number of edges in this shape is ______.
If the sum of number of vertices and faces in a polyhedron is 14, then the number of edges in that shape is ______.
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.
Using Euler’s formula, find the value of unknown p in the following table.
| Faces | p |
| Vertices | 6 |
| Edges | 12 |
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 |
Can a polyhedron have V = F = 9 and E = 16? If yes, draw its figure.
