Question : A solid has 12 vertices and 30 edges. How many faces does it have?
Option 1: 22
Option 2: 24
Option 3: 26
Option 4: 20
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Correct Answer: 20
Solution :
Given: Vertices = 12
Edges = 30
Let the vertices be V, edges be E and faces be F.
According to the Euler’s formula, V + F – E = 2
⇒ 12 + F – 30 = 2
⇒ F – 18 = 2
⇒ F = 18 + 2 = 20
Hence, the correct answer is 20.
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