Question

a right cone is intersected by a plane at an angle θ relative to the axis of the cone. which statements are true? select all that apply. a) for θ = 0°, the cross - section will be a triangle. b) for θ = 0°, the cross - section will be a rectangle. c) for θ = 0°, the cross - section will be a circle. d) for θ = 90°, the cross - section will be a circle. e) for θ = 90°, the cross - section will be a triangle.

Explanation:

Step1: Analyze $\theta = 0^{\circ}$ case

When a plane intersects a right - cone at an angle $\theta = 0^{\circ}$ relative to the axis of the cone, the plane is parallel to the base of the cone. The intersection of a plane parallel to the base of a cone is a circle.

Step2: Analyze $\theta = 90^{\circ}$ case

When a plane intersects a right - cone at an angle $\theta=90^{\circ}$ relative to the axis of the cone, the plane is perpendicular to the axis of the cone and passes through the vertex of the cone. The intersection of such a plane and a cone is a triangle.

Answer:

C. For $\theta = 0^{\circ}$, the cross - section will be a circle; E. For $\theta = 90^{\circ}$, the cross - section will be a triangle.