Advertisements
Advertisements
प्रश्न
A polyhedron can have 10 faces, 20 edges and 15 vertices.
पर्याय
True
False
उत्तर
This statement is False.
Explanation:
We know that, Euler's formula satisfies for every polyhedron.
i.e. F + V – E = 2
Here, F = 10, E = 20
And V = 15
On putting these values in the Euler's formula, we get
10 + 15 – 20 = 2
⇒ 25 – 20 = 2
⇒ 5 ≠ 2
Hence, the given values does not satisfy the Euler's formula.
APPEARS IN
संबंधित प्रश्न
Using Euler’s formula, find V if E = 30, F = 12.
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 the sum of number of vertices and faces in a polyhedron is 14, then the number of edges in that shape is ______.
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.
Using Euler’s formula, find the value of unknown q in the following table.
| Faces | 6 |
| Vertices | q |
| Edges | 12 |
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.
