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Can a Polyhedron Have 10 Faces, 20 Edges and 15 Vertices? - Mathematics

Answer in Brief

Can a polyhedron have 10 faces, 20 edges and 15 vertices?

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Solution

\[\text { No, because every polyhedron satisfies Euler's formula, given below: }\]

\[\text { F+V=E+2 }\]

\[\text { Here, number of faces F = 10 }\]

\[\text { Number of edges E = 20 }\]

\[\text { Number of vertices V = 15 }\]

\[\text { So, by Euler's formula: }\]

\[\text { LHS: 10+15 = 25 }\]

\[\text { RHS: 20 + 2 = 22 }, \]

\[\text { which is not true because 25 }\neq22\]

\[\text { Hence, Eulers formula is not satisfied and no polyhedron may be formed .}\]

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APPEARS IN

RD Sharma Class 8 Maths
Chapter 19 Visualising Shapes
Exercise 19.1 | Q 5 | Page 9
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