Name the following polyhedrons and verify the Euler’s formula for each of them.
Solution:
We have to name the given polyhedrons and verify the Euler’s formula for each of them.
Euler’s formula for any polyhedron is, F + V – E = 2
Where F stands for number of faces,
V for number of vertices
E for number of edges.
(a) The given figure is a Tetrahedron.
Number of faces = 4
Number of vertices = 4
Number of edges = 6
F + V - E = 4 + 4 - 6
= 8 - 6
= 2
(b) The given figure is a Cube.
Number of faces = 6
Number of vertices = 8
Number of edges = 12
F + V - E = 6 + 8 - 12
= 14 - 12
= 2
(a) The given figure is a Pentagonal prism.
Number of faces = 7
Number of vertices = 10
Number of edges = 15
F + V - E = 7 + 10 - 15
= 17 - 15
= 2
✦ Try This: Name the following polyhedron and verify the Euler’s formula.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 10
NCERT Exemplar Class 8 Maths Chapter 6 Sample Problem 12
Name the following polyhedrons and verify the Euler’s formula for each of them
Summary:
The name of the given polyhedron (a) Tetrahedron, (b) Cube, (c) Pentagonal prism. All the polyhedrons satisfy Euler's formula.
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