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Q.

How many faces does a dodecahedron have whose vertices are 20 and edges 30?


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a

12

b

24

c

20

d

30  

answer is A.

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Detailed Solution

Given, a dodecahedron have whose vertices are 20 and edges 30.
Question ImageEuler's polyhedron formula, -E+F=2 .
 V=number of vertices
 E=number of edges
 F=number of faces
Substitute the given values.
So, 20-30+F=2.
⇒ F-10=2 ⇒ F=10+2 ⇒ F=12 Number of faces =12.
Hence, option 1 is correct.
 
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How many faces does a dodecahedron have whose vertices are 20 and edges 30?