Multiple Choice Questions
1.Which of the following is a right pyramid?
C.II, III and IV only
D.I, II, III and IV
The base of a pyramid must be a polygon. Also, if all the slant edges of a pyramid are same in length, this pyramid is called a right pyramid. ∴II is a right pyramid.
2.If O is the foot of perpendicular of the vertex V of a nonagonal pyramid, find the angle between the straight line VO and the base.
∵VO is perpendicular to the base.
∴The angle between straight line VO and the base is 90(.
3.Which of the following are correct?
I.The base of a right triangular pyramid is a triangle. II.The lateral face of a right rectangular pyramid is a triangle. III.The lateral face of a right regular pentagonal pyramid is a regular pentagon.
C.I and II only
D.I, II and III
∵A right pyramid is named according to the shape of its base. ∴I is correct.
∵Each lateral face of a right pyramid is a triangle. ∴II is correct and III is incorrect.
4.How many planes of reflection are there in a right regular 21-gonal pyramid?
There are 21 planes of reflection in a right regular 21-gonal pyramid.
5.How many planes of reflection are there in a right regular 19-gonal prism?
There are 20 planes of reflection in a right regular 19-gonal prism.
6.If a solid has 8-fold rotational symmetry about the axis PQ, what should be the smallest angle of rotation of the solid about the axis PQ in order to coincide with itself?
Smallest angle of rotation [pic]
7.A right pyramid with a regular polygonal base has 9-fold rotational symmetry about the axis which passes through the vertex and the foot of perpendicular of the vertex. How many sides are there in the base of this pyramid?
For a right pyramid with a regular polygonal base, if it rotates about the axis which passes through the vertex and the foot of perpendicular of the vertex, the number of folds of rotational symmetry is equal to the number of sides of the base. ∴There are 9 sides in the base of the pyramid.
8.How many axes of rotation are there in a right regular nonagonal prism?
∴There are 10 axes of rotation in a right regular nonagonal prism.
9.The figure shows a regular tetrahedron. If it is cut along the grey edges, what is the net of the solid? [pic]
10.The figure shows a right regular pentagonal prism. If it is cut along the grey edges, what is the net of the solid? [pic]
11.If the following net is folded up to form a regular polyhedron, what kind of solid will you get? [pic]
A regular polyhedron is named according to the number of planes in the solid. As there are 8 equilateral triangles in the given net, it can be folded up to form a regular octahedron.