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Q.

Using Euler's formula, find the value of unknown x in the following table.


 Faces

7

 Vertices

10

 Edges

x


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a

4

b

7

c

15

d

10 

answer is C.

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Detailed Solution

Given that,
Number of faces = 7
Number of vertices = 10
Number of edges = x.
We know Euler’s formula for Polyhedron,
F + V = E + 2.
Where F is the number of faces, V denotes the number of vertices, and E denotes the number of edges.
Here,
F = Number of faces = 7
V = Number of vertices = 10
E = Number of edges = x.
According to Euler’s formula, we get
F + V = E + 2
⇒   7 + 10 = x + 2
⇒   17 = x + 2
⇒   x = 15
The number of edges = 15.
The correct option is (3).
 
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