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Q.

If the sum of the number of vertices and faces in a polyhedron is 16, then the number of edges in that shape is 12.


State true or false.


see full answer

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a

True

b

False 

answer is B.

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Detailed Solution

It is given a polyhedron.
Vertices+ faces =16.
According to Euler, there is a formula for Polyhedron.
For every polyhedron,
F = number of faces,
V = number of vertices,
E = number of edges.
According to Euler's Formula, F + V - E = 2.
Substituting the given values,
⇒   16 - E = 2
⇒   E = 14
The corrected statement is “If the sum of the number of vertices and faces in a polyhedron is 16, then the number of edges in that shape is 14”.
So, the given statement is false.
Hence, option 2 is correct.
 
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