Book: NCERT - Mathematics
Chapter: 10. Visualising Solid Shapes
Subject: Maths - Class 8th
Q. No. 8 of Exercises 10.3
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8
Can a polyhedron have 10 faces, 20 edges and 15 vertices?
Number of faces = F = 10
Number of edges = E = 20
Number of vertices = V = 15
Any polyhedron satisfies Euler's Formula, according to which, F + V - E = 2
For the given polygon,
F + V - E = 10 + 15 - 20
= 25 - 20
= 5 ≠ 2
Since Euler's formula is not satisfied, such a polyhedron is not possible
8
Chapter Exercises
More Exercise Questions
7
Using Euler’s formula find the unknown
Faces | ? | 5 | 20 |
Vertices | 6 | ? | 12 |
Edges | 12 | 9 | ? |