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Question
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 |
Solution
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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