12 multiple-choice questions, progressively harder.
Which description gives a prism?
Solution
Correct answer: B
A prism repeats the same polygon in a parallel plane and joins matching vertices.
A pyramid has an apex instead of a second congruent base, and circular bases do not make a polyhedron.
Which part of a polyhedron is an edge?
Correct answer: D
An edge is a straight segment shared by faces.
A corner is a vertex. A circular rim belongs to a curved-solid description, not to the straight-edge counts for polyhedra.
How many faces, edges, and vertices does a cube have, in that order?
Correct answer: A
The top and bottom contribute two faces, and four faces join them. The two square boundaries contribute eight edges, and four more edges join corresponding corners.
Thus the counts are 6 faces, 12 edges, and 8 vertices.
A triangular prism has two triangular bases. How many vertices does it have?
Correct answer: C
Each triangular base has three vertices. The two bases lie in distinct parallel planes, so none of their vertices coincide.
There are six vertices.
A square pyramid has one square base and an apex off its plane. How many faces does it have?
The base is one face. Each of its four edges joins the apex to make a triangular face.
There are five faces.
Which property makes a prism right?
The base-plane relationship defines a right prism.
Page orientation can change when the solid is turned, and the bases can be polygons other than squares.
Which description distinguishes skew lines from parallel lines?
Skew lines do not lie in one plane.
Parallel lines are coplanar. An apparent crossing in a projection does not determine whether the actual lines meet.
Two distinct planes share two distinct points. What must their intersection be?
Each plane contains the complete line through the two points.
Distinct intersecting planes have exactly one line in common, so the intersection continues beyond the segment shown.
Why is a cylinder not a polyhedron?
A polyhedron has a surface made entirely of polygonal faces.
A cylinder has a curved side and circular bases, so it fails that requirement.
What must a net of a closed polyhedron do when folded?
A net supplies every face once and folds to the complete boundary.
Cut edges can meet again on closing, but face interiors must not overlap.
Which two dimensions does a front orthographic view record?
Looking from front toward back projects away the depth direction.
The front view retains left-to-right width and vertical height.
Which statement uses sphere and ball precisely?
A sphere consists of points at one fixed positive distance from its center.
A ball also includes the points closer to the center, so it contains the enclosed region.
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