State and verify the Euler's Formula for a rectangular prism. What will be the number of faces of a polyhedron if the number of vertices are 6 and number of edges are 12 ?
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40
Ans. 1.
No. of faces of rectangular prism = 5
No.of vertices of rectangular prism = 5
No. of edges of rectangular prism = 8
now,
Euler's Formula=> F + V = E + 2
=> 5 + 5 = 8 +2
=> 10 = 10
So, it is verified by Euler's Formula.
Ans. 2.
No. of faces of polyhedron. = F
No.of vertices of polyhedron = 6
No. of edges of polyhedron. = 12
So, again
Euler's Formula=> F + V = E + 2
=> F + 6 = 12+2
=> F = 14-6
=> F = 8
So, the no. of faces in polyhedron which have 6 vertices and 12 edges is "8".
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246
Euler's polyhedron formula, V−E+F=2
V = number of vertices = 6
E = number of edges = 12
F = number of faces = ?
6−12+F=2
F=6+2
F=8
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