A polyhedron has $11$ faces and $18$ vertices. Find the number of edges.

15

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27

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33

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21

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Solution

The correct option is D $27$
Euler's Formula
For any polyhedron that doesn't intersect itself, the
Number of Faces
plus the Number of Vertices (corner points)
minus the Number of Edges
always equals 2
This can be written: F + V − E = 2
Using this $11 + 18 - E = 2$
$\Rightarrow E = 27$

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