What cross sections might you see when a plane intersects a sphere that you would not see when a plane intersects
pyramid or a prism?
circles, of course.
When a plane intersects a solid object, the resulting cross section will depend on the shape of the object and the orientation of the plane. In the case of a sphere, there are a few specific cross sections that you might see which are not possible when intersecting a pyramid or a prism.
1. Circle: Since a sphere is a three-dimensional object with a curved surface, one common cross section you would see is a circle. If the plane passes straight through the center of the sphere, the resulting cross section will be a perfect circle.
2. Ellipse: If the plane intersecting the sphere is at an angle to the axis of the sphere, the resulting cross section will be an ellipse. The size and shape of the ellipse will depend on the angle and position of the plane relative to the sphere.
These two cross sections, a circle and an ellipse, are specific to intersecting a sphere and are not possible when intersecting a pyramid or a prism.