Cone from a sector

You can do this with paper, scissors, and tape. In this simulation, adjust the angle of the sector with point B. Change the radius with point D. The rolled-up cone is shown at right. The green radii are shown as a green segment on the cone, and the red arc becomes the red circle at the base of the cone. Some questions to think about (and maybe experiment with paper):
  • How can you make a cone with a specific size of circular base (say, for a hat that fits your head)?
  • How can you make a cone with a specific angle at the top point, if viewed from the side?
  • If you make cones from circles with the same radii, which will hold the most (have the greatest volume)? If you make several cones, you can compare them by filling them with uncooked rice or beans (if they are small) or popped popcorn (if they are big).