Question

a solid is cut by a vertical plane, forming a two - dimensional cross section in the shape of a circle. which of the following solids could have resulted in that cross section?
answer
sphere
right cone
triangular pyramid
right pentagonal prism

Explanation:

To determine which solid can have a circular cross - section when cut by a vertical plane:

• A sphere: Any plane that cuts a sphere will form a circular cross - section. This is because a sphere is a perfectly round three - dimensional object, and the intersection of a plane and a sphere is always a circle.
• A triangular pyramid: A triangular pyramid (tetrahedron) has triangular faces. When cut by a plane, the cross - section will be a triangle or a polygon, but never a circle, since it has no curved surfaces.
• A right cone: A right cone has a circular base, but when cut by a vertical plane (assuming the plane is along the axis of symmetry), the cross - section is a triangle. If the plane is not along the axis of symmetry, the cross - section is an ellipse (not a circle in general). Only when the plane is perpendicular to the axis of the cone (horizontal plane) will the cross - section be a circle. But the question specifies a vertical plane. However, for a sphere, any vertical plane (or any plane) will give a circular cross - section.
• A right pentagonal prism: A right pentagonal prism has pentagonal and rectangular faces. When cut by a plane, the cross - section will be a pentagon, rectangle, or other polygon, not a circle, as it has no curved surfaces.

Answer:

sphere