Mathematics
Assertion (A) : The number of edges in a rectangular pyramid = 8.
Reason (R) : In a triangular prism, the number of vertices is one more than number of sides and the number of faces is one less than number of sides.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are false.
A is true, but R is false.
A is false, but R is true.
Answer
A rectangular pyramid has 5 faces, 8 edges, and 5 vertices.
So, assertion (A) is true.
A triangular prism has 5 faces, 9 sides, and 6 vertices.
Difference between sides and vertices = 9 - 6 = 3
Difference between sides and faces = 9 - 5 = 4
So, reason (R) is false.
∴ A is true, but R is false.
Hence, option 3 is the correct option.
Related Questions
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.
Draw the net of a rectangular box.
Can a polyhedron have 15 faces, 30 edges and 20 vertices ?