Advertisements
Advertisements
प्रश्न
If a solid shape has 12 faces and 20 vertices, then the number of edges in this solid is ______.
उत्तर
If a solid shape has 12 faces and 20 vertices, then the number of edges in this solid is 30.
Explanation:
We know that, Euler's formula for any polyhedron is F + V – E = 2
Given, faces, F = 12, vertices, V = 20
Now, on putting the value of F and V in the Euler's formula, we get 12 + 20 – E = 2
⇒ 32 – E = 2
⇒ 32 – 2 = E
⇒ E = 30
Hence, the number of edges = 30
APPEARS IN
संबंधित प्रश्न
In a solid if F = V = 5, then the number of edges in this shape is ______.
Euler’s formula is true for all three-dimensional shapes.
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 |  |
|||||
| b. | Triangular Pyramid |
 |
|||||
| c. | Square Pyramid |
 |
|||||
| d. | Rectangular Pyramid |
 |
|||||
| e. | Pentagonal Pyramid |
 |
|||||
| f. | Hexagonal Pyramid |
 |
|||||
| g. | Triangular Prism |
 |
|||||
| h. | Square Prism |
 |
|||||
| i. | Cube |  |
|||||
| j. | Pentagonal Prism |
 |
|||||
| k. | Octagonal Prism |
 |
|||||
| l. | Heptagonal Prism |
 |
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.
A polyhedron has 60 edges and 40 vertices. Find the number of its faces.
A polyhedron has 20 faces and 12 vertices. Find the edges of the polyhedron.
