Advertisements
Advertisements
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 |
Advertisements
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
APPEARS IN
RELATED QUESTIONS
If a solid shape has 12 faces and 20 vertices, then the number of edges in this solid is ______.
Euler’s formula is true for all three-dimensional shapes.
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.
Using Euler’s formula, find the value of unknown p in the following table.
| Faces | p |
| Vertices | 6 |
| Edges | 12 |
Using Euler’s formula, find the value of unknown r in the following table.
| Faces | 8 |
| Vertices | 11 |
| Edges | r |
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.
