To determine the shape of the cross-section when a plane intersects a sphere, let's think about the geometric properties involved.
1. A sphere is a perfectly round 3-dimensional shape.
2. When a plane intersects any solid object, the intersection will be a 2-dimensional shape.
3. Now, consider different positions of the intersecting plane:
- If the plane intersects the sphere in such a way that it does not pass through the center, it still cuts the sphere into two identical halves, creating a circular cross section.
- If the plane intersects exactly through the center of the sphere, it will also create a circular cross section.
Given these considerations, regardless of how the plane intersects the sphere (whether through the center or not), the resulting cross-section will always be a circle.
Hence, the correct answer is:
D. a circle
