Mathematics
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.
3D in 2D
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Answer
The base of a pyramid is a polygon. Let no. of sides in polygon be n, so total number of vertices in a polygon will be n.
So, the total number of vertices in a pyramid will be n + 1.
So, statement 1 is true.
Given,
A polyhedron may have 10 faces 20 edges and 15 vertices.
If this is true, then it will satisfy Euler's formula.
Using Euler's formula :
F + V - E = 2.
Substituting the values in L.H.S., we get
⇒ 10 + 15 - 20
⇒ 25 - 20
⇒ 5
R.H.S. = 2
Since, L.H.S. ≠ R.H.S.
So, statement 2 is false.
∴ Statement 1 is true, and statement 2 is false.
Hence, option 3 is the correct option.
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Related Questions
In case of a hexagonal pyramid, F = no. of faces and V = no. of vertices, then F + V is:
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The number of faces in a triangular pyramid is :
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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.
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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.
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A is false, but R is true.