Practical Exercise 1: MAKE A CONE AND CUT YOUR OWN CONIC SECTIONS.
Aim:
To illustrate how the conic sections are produced. This activity can be done individually or in pairs.
Necessary materials:
- a sheet of card stock or thicker paper (size A5),
- same size sheet of parchment,
- pencil compass,
- scissors,
- tape,
- air-dry modeling clay,
- dental floss (about 40 cm).
Instructions for the teacher:
The students have to draw a half-circle on the card stock and parchment and cut it out to form a cone. The parchment come is placed within the card stock cone and filled with the clay. Then the resultant cone is removed from the cover. Then with the dental floss, the conic sections can be cut out. It will be difficult to cut out all the sections one after another, so the cone might have to be reassembled at least once.
Instructions for the students:
1. On the card stock and parchment, find the middle of the long side and mark it with the pencil. This will be the centre of your half-circle.
2. Draw a half-circle on both the card stock and parchment, each with radius of 9 cm using the pencil compass.
3. Cut them out, curl them to form a cone and secure each cone with tape. Place the parchment cone within the card stock cone.
4. Pack cone to the top with air-dry modeling clay. Use small pieces and press down to the tip of the cone. You can pull the parchment paper out a little to peek as you go, to make sure there aren’t any big gaps or air bubbles. Flip over onto a paper plate or sheet of parchment paper. Remove card stock cone, then peal away the parchment paper.
5. Once you have your cone you can use dental floss to make your sections. Cut straight across near the top to make a circle.
6. Below your circle, make a slanting cut to make your ellipse. Do not slant the floss too much.
7. If you had cut out the ellipse too far down, reform the cone.
8. Make a cut that slants enough to pass through the bottom of the cone to make your parabola.
9. Do another cut that goes straight down, but without the top cone to make a hyperbola.
Summary questions:
Q: Which section in perpendicular to the axis of the cone?
A: The circle.
Q: Which section is parallel to the slant of the cone?
A: The parabola.
Q: How can you make circles with different radii?
A: By cutting the cone at different distances from the top (base).
Q: Which circle has the biggest radius in a cone?
A: Its base.
