Look at the shapes given below 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 = 6, Vertices = 8, and Edges = 12
Now, F + V - E = 6 + 8 − 12
= 14 - 12
= 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 = 7, Vertices = 10, and Edges = 15
Now, F + V - E = 7 + 10 − 15
= 17 - 15
= 2
Therefore, it is a polyhedron.
✦ Try This: Can a polyhedron have F = V = 9 and E = 16.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 10
NCERT Exemplar Class 8 Maths Chapter 6 Problem 67 (a)
Look at the shapes given below 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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