Look at the shapes given and state which of these are polyhedra using Euler’s formula.
Solution:
We have to determine which of the given solids are polyhedron by using Euler’s formula.
Euler’s formula for any polyhedron is given by
F + V - E = 2
Where F stands for number of faces,
V for number of vertices
E for number of edges.
From the figure,
Faces = 8, Vertices = 6, and Edges = 12
Now, F + V - E = 8 + 6 − 12
= 14 - 12
= 2
Therefore, it is a polyhedron.
From the figure,
Faces = 2, Vertices = 1, and Edges = 0
Now, F + V - E = 2 + 1 − 0
= 3 - 0
= 3
Therefore, it is not a polyhedron.
From the figure,
Faces = 10, Vertices = 16, and Edges = 24
Now, F + V - E = 10 + 16 − 24
= 26 - 24
= 2
Therefore, it is a polyhedron.
From the figure,
Faces = 1, Vertices = 0, and Edges = 1
Now, F + V - E = 1 + 0 − 1
= 1 - 1
= 0
Therefore, it is not a polyhedron.
✦ Try This: Can a polyhedron have F = V = 10 and E = 18.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 10
NCERT Exemplar Class 8 Maths Chapter 6 Problem 67 (c)
Look at the shapes given and state which of these are polyhedra using Euler’s formula.
Summary:
Each of the given shapes are verified using Euler’s formula and the polyhedra are mentioned above.
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