## Saturday, June 20, 2009

### Tutorial: Modular Paper Cone

Paper cones are versatile for crafting.
- tip down, they serve as hanging vases
- holiday paper cones can represent trees
- they make great party hats

It's simple to roll paper into a cone. But what if you want to make a cone that's a specific radius and height? What if you want the base to sit evenly on a flat surface?

Making custom cones is simple and only uses a little math. To make it more accessible (that is, to prevent your eyes from glazing over), I will simply give the instructions here. I plan to post an explanation of the calculations on my Family Math blog.

Step One: Determine the radius (r) of your base and the height. You'll use these to find the "slant height". This online calculator will do it for you: Calculator. Just enter the radius of the base and the height as the sides. The result (hypotenuse) is your slant height: s. (If you know a little geometry, this slant height is calculated using the Pythagorean Theorem.)

Step Two: Determine the angle of the wedge shape you'll need to cut from paper. This another simple calculation: Angle=360r/s
(r is the radius of the base, s is the slant height from the previous step)

Step Three: You will be drawing this angle on your paper. To do this, select a point for the vertex of the angle. Draw one line that starts at the point and is length s.

Using a protractor, mark a point that makes the angle you determined from this point. Draw a line that connects the point to this line and extends beyond it for length S. At this point, you should have an angle with two legs of equal length on your paper.

Step Four: To draw the arc which will be the edge of your cone's base, you will need a compass*. Adjust your compass so the distance it spans is the same as the slant height, s. Place the point of your compass on the vertex of your angle and sketch the arc.

Step Five: Make a tab along one side of the wedge, as shown. This will be the gluing tab. I added the red lines to this picture to show the details. Notice, I cut the tab short on the point side.

Step Six: Cut out the wedge, roll into a cone and glue together.

*(You can also substitute a strip of paper a little longer than S for the compass. Place the paper to be cut onto cork board or some other surface you can pin into. Mark a line on the strip that is the same length as S. Make a small hole in one end of the line. Then pin the other end of the line through the vertex of your angle. Place a pencil into the hole and make your arc line.)