Mathematics
Assertion (A) : In a polyhedron, there are 6 vertices, 12 edges then the number of faces are 8.
Reason (R) : In a pentagonal pyramid there are 6 faces, 6 vertices and 10 edges.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
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Answer
In assertion (A),
Given,
E = 12 and V = 6.
Using Euler's formula :
⇒ F + V - E = 2.
Substituting the values, we get :
⇒ F + 6 - 12 = 2
⇒ F - 6 = 2
⇒ F = 2 + 6
⇒ F = 8
So, assertion (A) is true.
In reason (R),
Given,
F = 6, E = 10, and V = 6.
Using Euler's formula :
⇒ F + V - E = 2.
Substituting the values in L.H.S., we get
⇒ 6 + 6 - 10
⇒ 12 - 10
⇒ 2
R.H.S. = 2
Since, L.H.S. = R.H.S.
So, reason (R) is true.
∴ Both A and R are correct, and R is not the correct explanation for A.
Hence, option 2 is the correct option.
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Related Questions
The number of faces in a triangular pyramid is :
3
4
5
none of these
Statement 1: The number of vertex in a pyramid is one more than the number of sides in a polygon.
Statement 2: A polyhedron may have 10 faces 20 edges and 15 vertices.
Which of the following options is correct?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Assertion (A) : If a polyhedron has 7 vertices and 10 faces, the number of edges is 19.
Reason (R) : The relationship between faces (F), edges (E) and vertices (V) of a polyhedron is F + V - E = 2.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Assertion (A) : The number of edges in a triangular prism = 9.
Reason (R) : In a triangular prism, the number of vertices = 2 x number of sides = 6;
The number of faces = 2 + number of sides = 5.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.