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Visualising Shapes — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsVisualising Shapes3 Marks
Question
Can a polyhedron have 10 faces, 20 edges and 15 vertices?
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Answer

No, because every polyhedron satisfies Euler's formula, given below:
F + V = E + 2 Here, number of faces F = 10
Number of edges E = 20
Number of vertices V = 15
So, by Euler's formula:
LHS: 10 + 15 = 25
RHS: 20 + 2 = 22,
which is not true because $25\neq22$
Hence, Eulers formula is not satisfied and no polyhedron may be formed.

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