A student argues that a sphere must have more vertices than a cone because it is rounder and more complicated. Which response is correct?
AThe student is right — a sphere's curved complexity gives it more vertices than the cone's one
BThey are equal — both a sphere and a cone have exactly one vertex
CThe student is wrong — a sphere has 0 vertices and a cone has exactly 1 vertex at its tip
DA cone has more vertices than a sphere because sharp angles always count as vertices
A sphere has no vertices at all — it is perfectly round with no corners or points anywhere on its surface. A cone has exactly 1 vertex at its pointed tip. The misconception is that a more complex-looking shape must have more vertices, but vertex count depends on structure, not visual complexity.
Question 2 Multiple Choice
Which set of attributes correctly describes a rectangular prism like a cereal box?
A4 faces, 8 edges, 6 vertices
B6 faces, 12 edges, 8 vertices
C6 faces, 8 edges, 12 vertices
D8 faces, 12 edges, 6 vertices
A rectangular prism has 6 flat faces (top, bottom, front, back, left, right), 12 edges (where those faces meet), and 8 vertices (the corners). A cube has the same counts — it is just a special rectangular prism where all faces are squares.
Question 3 True / False
A cylinder has more edges than a cone.
TTrue
FFalse
Answer: True
A cylinder has 2 edges — the two circles where the flat circular faces meet the curved side. A cone has only 1 edge — the circle where the flat circular base meets the curved side. So yes, a cylinder (2 edges) has more edges than a cone (1 edge).
Question 4 True / False
A sphere and a cube both have vertices.
TTrue
FFalse
Answer: False
A cube has 8 vertices (its 8 corners). A sphere has zero vertices — it is perfectly round with no corners anywhere. This statement is false because the sphere has no vertices at all.
Question 5 Short Answer
Explain what a face, an edge, and a vertex are on a 3D shape. Give an example of each using a cube.
Think about your answer, then reveal below.
Model answer: A face is a flat surface — a cube has 6 flat square faces. An edge is the line where two faces meet — a cube has 12 edges. A vertex is the point (corner) where three or more edges come together — a cube has 8 vertices.
These three types of parts describe every 3D shape. Faces are flat surfaces, edges are where faces join, and vertices are the corner points. Counting each type precisely is how mathematicians describe the properties of geometric solids — going beyond just naming a shape to describing what makes it that shape.