Making Cross Sections of a Sphere

This interactive GeoGebra example demonstrates how slicing a sphere with a plane produces different cross-sectional shapes. The core mathematical concept is solid geometry, specifically cross sections of three-dimensional figures. Users can visually explore that every cross section of a sphere is a circle (including a point when the plane is tangent), and investigate how the size of the circle changes with the plane's position and orientation. The construction uses GeoGebra commands such as Sphere to create the solid, Plane to define the cutting plane, IntersectPath to compute the intersection curve, and Circle to display the resulting cross section. Interactive elements include sliders and a dropdown menu (SelectedIndex) to adjust the plane dynamically. This resource is suitable for middle school to high school students (grades 6-8 and above) learning geometry, and is also valuable for teachers demonstrating spatial reasoning in the classroom. It encourages open-ended questions, such as listing possible cross-section shapes and evaluating whether all cross sections have the same area.