Advertisements
Advertisements
प्रश्न
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 |
Advertisements
उत्तर
We will solve for x, y, and z using Euler's formula for polyhedra:
V − E + F = 2
Where:
- V = Number of vertices,
- E = Number of edges,
- F = Number of faces.
(i) Find x (Number of Faces)
- V = 15,
- E = 20
- F = x
Using Euler's formula:
15 − 20 + x = 2
−5 + x = 2
x = 7
(ii) Find y (Number of Vertices)
- V = y,
- E = 8
- F = 6
Using Euler's formula:
y − 8 + 6 = 2
y − 2 = 2
y = 4
(iii) Find z (Number of Edges)
Given:
- V = 26,
- E = z
- F = 14
26 − z + 14 = 2
40 − z = 2
z = 38
Final Answers:
- x = 7,
- y = 4
- z = 38
APPEARS IN
संबंधित प्रश्न
Verify Euler’s formula for the following three-dimensional figures:
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.
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.
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 y in the following table.
| Faces | y |
| Vertices | 12 |
| Edges | 18 |
Using Euler’s formula, find the value of unknown r in the following table.
| Faces | 8 |
| Vertices | 11 |
| Edges | r |
