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Q.

An icosahedron has 30 edges and 12 vertices. How many faces does it have?


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a

10

b

20

c

30

d

40 

answer is B.

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Detailed Solution

Given, an icosahedron has 30 edges and 12 vertices.
Number of faces can be found using Euler’s polyhedron formula.
Euler's polyhedron formula, V-E+F=2.
V = number of vertices
E = number of edges
F = number of faces
So, 12-30+F=2.
⇒ F-18=2 ⇒ F=18+2 ⇒ F=20 Number of faces = 20.
Hence, option 2 is correct.
 
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