Advertisements
Advertisements
Question
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
Advertisements
Solution
In the given figure, we have
Faces (F) = 3, Vertices (V) = 0 and Edges (E) = 2
On putting these values in Euler’s formula, we get
F + V – E = 2
⇒ 3 + 0 – 2 = 2
⇒ 1 ≠ 2
Hence, these values do not satisfy the Euler’s formula. So, it is not a polyhedra.
APPEARS IN
RELATED QUESTIONS
Verify Euler’s formula for the following three-dimensional figures:
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 |
In a solid if F = V = 5, then the number of edges in this shape is ______.
Euler’s formula is true for all three-dimensional shapes.
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 z in the following table.
| Faces | 9 |
| Vertices | z |
| Edges | 16 |
A polyhedron has 20 faces and 12 vertices. Find the edges of the polyhedron.
