Question

3-d solids have vertices
□ cube
□ triangular pyramid
□ sphere
□ cylinder
□ no counter-example listed

Explanation:

To determine which 3 - D solids are counter - examples to the statement "3 - D solids have vertices", we analyze each solid:

• A cube has 8 vertices. So it does not counter the statement.
• A triangular pyramid (tetrahedron) has 4 vertices. So it does not counter the statement.
• A sphere is a perfectly round 3 - D object with no distinct vertices (points where edges meet).
• A cylinder has two circular faces and a curved surface. It does not have vertices (in the traditional sense of points where edges meet).
• The option "No counter - example listed" is incorrect as we have identified counter - examples.

So the counter - examples are Sphere and Cylinder. But if we have to choose from the given options as per the question's context (maybe choosing one of the counter - examples), Sphere and Cylinder are the ones that do not have vertices. But looking at the options, if we consider the most appropriate counter - example, Sphere and Cylinder both fit. However, if we have to mark the correct ones (assuming the question is to find which of these do not have vertices to counter the statement), the correct options are:

Answer:

B. Sphere, C. Cylinder