Look at the shapes 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 = 5, Vertices = 6, and Edges = 9
Now, F + V - E = 5 + 6 − 9
= 11 - 9
= 2
Therefore, it is a polyhedron.
From the figure,
Faces = 3, Vertices = 0, and Edges = 2
Now, F + V - E = 3 + 0 − 2
= 3 - 2
= 1
Therefore, it is not a polyhedron.
From the figure,
Faces = 11, Vertices = 11 and Edges = 20
Now, F + V - E = 11 + 11 − 20
= 22 - 20
= 2
Therefore, it is a polyhedron.
From the figure,
Faces = 9, Vertices = 9, and Edges = 16
Now, F + V - E = 9 + 9 − 16
= 18 - 16
= 2
Therefore, it is a polyhedron.
From the figure,
Faces = 8, Vertices = 12, and Edges = 18
Now, F + V - E = 8 + 12 − 18
= 20 - 18
= 2
Therefore, it is a polyhedron.
✦ Try This: Can a polyhedron have F = 8, V = 10 and E = 14.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 10
NCERT Exemplar Class 8 Maths Chapter 6 Problem 67 (b)
Look at the shapes 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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