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?[br][br]What cross-section is formed when the plane passes through the apex? Is this true for any pyramid or only cones?[br][br]What extra information would you need to find the relationship between slant height and perpendicular height?[br][br]What is the rule which relates slant height to perpendicular height?