Determine the number of edges, vertices and faces in the following figure:
Solution:
We have to find the number of faces, edges and vertices in the given figure.
The given figure has equal length, width and height.
Therefore, the given figure is a Cube.
The polygonal regions are called faces.
Number of faces in the cube = 7
The line segment formed by the intersection of two faces is called edges.
Number of edges = 15
Vertex is a point where two or more edges meet.
Number of vertices = 10
Verification:
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.
Now, F + V = E + 2
LHS: F + V
F + V = 7 + 10
= 17
RHS = E + 2
E + 2 = 15 + 2
= 17
LHS = RHS
Therefore, the number of faces, vertices and edges are 7, 10 and 15.
✦ Try This: Determine the number of edges, vertices and faces in the following figure:
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 10
NCERT Exemplar Class 8 Maths Chapter 6 Sample Problem 18
Determine the number of edges, vertices and faces in the following figure.
Summary:
The number of faces, edges and vertices in the given figure are 7, 15 and 10.
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