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Is it true that the given shape is polyhedral using Euler’s formula?

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True

False

answer is B.

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Detailed Solution

Given solid is,
Question Image

To check given shape is polyhedron we have to undergo Euler’s formula for polyhedron.
We know that, Euler’s formula for any polyhedron is

F + V - E = 2

where

F

is face of the polyhedron,

V

is the vertices of the polyhedron, and

E

is the edges of the polyhedron.
In the figure,

F = 2, V = 1 and E = 0

.
On putting above values in Euler’s formula,

2 + 1 - 0 = 2

\Rightarrow 3 \neq 2

So, given values does not satisfy Euler’s formula that means given shape is not polyhedron.
The given shape is not polyhedral.
Therefore, the given statement is false.
Hence, option (2) is correct.

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