Is it true that a polyhedron has 20 faces and 12 vertices then the number of edges of the polyhedron is 30?

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True

False

answer is A.

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Detailed Solution

It is given that,
Polyhedron has 20 faces and 12 vertices.
Then,

Number of faces, F = 20

Number of vertices, V = 12

.
We know that Euler’s formula for any polyhedron is

F + V - E = 2

where F is the face of the polyhedron, V is the vertices of the polyhedron and E is the edges of the polyhedron.
On putting given values in Euler’s formula,

20 + 12 - E = 2

\Rightarrow 32 - E = 2

\Rightarrow E = 32 - 2

\Rightarrow E = 30

So, the edges of the polyhedron are 30.
Therefore, the given statement is true.
Hence, option (1) is correct.

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