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Q.

Is Euler's formula true for pentagonal prism?


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a

    True

b

    False 

answer is A.

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Detailed Solution

It is given a pentagonal prism.
According to Euler's Formula, F + V - E = 2.
Where F = number of faces,
V = number of vertices,
E = number of edges.
A Pentagonal prism is a polyhedron with 10 vertices, 15 edges, and 7 faces.
Number Faces = F = 7
Number of edges = E = 15
Number of vertices = V = 10
Now take, LHS = F + V - E
⇒   7 + 10 -15
⇒   17 - 15
⇒   2
We know RHS = 2.
So, LHS = RHS
Hence, Euler's Formula is true for pentagonal prisms.
Correct option is 1.
 
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Is Euler's formula true for pentagonal prism?