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 will create a cross - section congruent to the base. Since the base is a 9 - sided polygon, the cross - section will also be a 9 - sided polygon, 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 be a rectangle (or a polygon with a number of sides related to the intersection with the two edges and the base, but not 10 - sided). The maximum number of sides in this case will be related to the number of sides of the base and the two edges, but it won't be 10. So B is incorrect.
• Option C: If the plane is perpendicular to the base and contains one edge of the prism, the cross - section will be a polygon with a number of sides related to the base and the one edge, but not 10 - sided. So C is incorrect.
• Option D: When the plane makes a narrow angle with the base, it can intersect more faces of the prism. A 9 - sided prism has 9 lateral faces and 2 bases. To get a 10 - sided cross - section, the plane needs to intersect 10 faces. When the plane is at a narrow angle to the base, it can intersect 9 lateral faces and 1 base face (or a combination that results in 10 intersections), creating a 10 - sided polygon.

Answer:

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