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
Answers
Answer: The answer is (D) when the plane makes a narrow angle with the base.
Step-by-step explanation: Given that a prism whose base is a 9-sided polygon is intersected by a plane. We need to find the case from the given options when the cross section will be a 10-sided polygon.
(A) When the plane is parallel to the base of the prism, then the cross-section will be congruent to the base. That is, it will be a 9-sided polygon.
(B) When the plane is perpendicular to the base and contains two edges of the prism, then the cross-section will be a parallelogram.
(C) When the plane is perpendicular to the base and contains one edge of the prism, then also the cross-section will be a parallelogram.
(D) Wen the plane makes a narrow angle with the base, then the cross-section will be a 10-sided polygon. Here, the plane will cut one base and 8 edges of the prism so that the intersection will be at 10 points resulting in a 10-sided polygon.
Thus, (D) is the correct option.