Advertisements
Advertisements
Question
In a solid if F = V = 5, then the number of edges in this shape is ______.
Options
6
4
8
2
Advertisements
Solution
In a solid if F = V = 5, then the number of edges in this shape is 8.
Explanation:
Euler’s formula for any polyhedron is F + V – R = 2
Given, F = V = 5
On putting the values of F and V in the Euler’s formula, we get
5 + 5 – E = 2
⇒ 10 – E = 2
⇒ E = 8
Notes
F = Faces, V = Verticles and E = Edges
APPEARS IN
RELATED QUESTIONS
Using Euler’s formula, find V if E = 30, F = 12.
Verify Euler’s formula for the following three-dimensional figures:
Which of the following cannot be true for a polyhedron?
If a solid shape has 12 faces and 20 vertices, then the number of edges in this solid is ______.
A polyhedron can have 10 faces, 20 edges and 15 vertices.
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.
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
