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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 |
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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
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संबंधित प्रश्न
Verify Euler’s formula for the following three-dimensional figures:
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 ______.
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.
Check whether a polyhedron can have V = 12, E = 6 and F = 8.
A solid has forty faces and sixty edges. Find the number of vertices of the solid.
