Cross-Sections of cones

Topic:
Cone
Students can experiment with the different cross-sections formed through passing a plane through a cone
How many different types of cross sections can you find? What cross-section is formed when the plane passes through the apex? Is this true for any pyramid or only cones? What extra information would you need to find the relationship between slant height and perpendicular height? What is the rule which relates slant height to perpendicular height?