Question

select the correct answer.

a prism whose base is a 9 - sided polygon is intersected by a plane. in which case could the cross section be a 10 - sided polygon?

a. when the plane is parallel to the base of the prism

b. when the plane is perpendicular to the base and contains two edges of the prism

c. when the plane is perpendicular to the base and contains one edge of the prism

d. when the plane makes a narrow angle with the base

Explanation:

• Option A: A plane parallel to the base of a prism with a 9 - sided base will produce a cross - section that is also a 9 - sided polygon (congruent to the base), so A is incorrect.
• Option B: If the plane is perpendicular to the base and contains two edges of the prism, the cross - section will have fewer than 10 sides. The intersection with the two edges and the base will not result in a 10 - sided figure, so B is incorrect.
• Option C: A plane perpendicular to the base and containing one edge will also not produce a 10 - sided cross - section. The number of sides will be related to the intersection with the edge and the base, and it will not be 10, so C is incorrect.
• Option D: When the plane makes a narrow angle with the base, it will intersect 10 faces of the prism (9 faces of the base - related part and 1 additional face due to the angle). A prism with a 9 - sided base has 9 lateral faces and 2 bases. When the plane is at a narrow angle, it can intersect 10 faces, resulting in a 10 - sided cross - section.

Answer:

D. when the plane makes a narrow angle with the base