Advertisements
Advertisements
प्रश्न
Using Euler’s formula, find the value of unknown p in the following table.
| Faces | p |
| Vertices | 6 |
| Edges | 12 |
Advertisements
उत्तर
By using Euler’s formula for polyhedron
From, V = 6, E = 12 and F = p
So, F + V – E = 2
⇒ p + 6 – 12 = 2
⇒ p – 6 = 2
⇒ p = 2 + 6
⇒ p = 8
APPEARS IN
संबंधित प्रश्न
Using Euler’s formula, find V if E = 30, F = 12.
In a solid if F = V = 5, then the number of edges in this shape is ______.
If a solid shape has 12 faces and 20 vertices, then the number of edges in this solid 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.
Using Euler’s formula, find the value of unknown x in the following table.
| Faces | 7 |
| Vertices | 10 |
| Edges | x |
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 |
