Now, let’s investigate cross sections and slices of cones.

Return to the sketch on the link Cross Section Flyer.

1. Click on the radio button next to Cone.


2. Click on the Rotate slice around Y slider until the slice, represented by the red portion of the figure, is parallel to the base.


3. Click on the Move slice slider. What do you observe as the slice moves up and down the figure? You can also click the Animate button to automatically move the slice.


4. What shape is the slice? How does this shape compare with the base of the cone?


5. Change the angle between the plane of intersection and the base by clicking on the Rotate slice around Y slider.


6. Move the slice (remember – it’s not parallel to the base anymore, so it’s technically not a cross-section) up and down the cone using the Move slice slider. Change the angle by clicking on the Rotate slice around Y slider. What other shapes can be generated by slicing a cone? Use a table like the one shown to summarize your findings. You may create the table in your notes.
   
   

   Shape of Slice	Intersection with Base and Lateral Surfaces

Journal Entry

What patterns and relationships do you observe between the possible shapes of slices of cones when the angle of intersection is parallel or is not parallel to the base of the cone?

How do the slices and cross-sections of cones compare to those of pyramids?