# How to Layout a Cone Shape

Written by paul dohrman
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A cone is a popular shape for party hats, Christmas trees, and other useful or decorative objects. Therefore, it can be helpful to be able to draw a pattern or template for a cone of a height and width of one's choosing. The cone is created from a circular piece of paper or cloth by cutting a pie-type wedge out. The size of the circle and the wedge will determine the height and width of the cone.

Skill level:
Moderate

### Things you need

• Calculator
• Pencil
• Compass
• Paper, poster board or cloth
• Scissors
• Ruler
• Tack and string (optional)
• Protractor
• Glue or tape

## Instructions

1. 1

Decide on the height, H, and width, W, you want for the cone you will make.

2. 2

Use the height and width to calculate what the radius, R, of the circle the cone will be made from should be. The formula for finding the radius is R = √[0.25W^2+H^2]. In this formula √ tells you to take the square root of the quantity in brackets. The caret ^ indicates exponentiation--W^2 is the width squared, and H^2 is the height squared.

3. 3

Mark where the centre of the circle will be on the material that you're making the cone out of.

4. 4

Draw a circle on the cone material using either a compass or a tack and string. To use the compass, place its sharp end at the centre of the circle and place the pencil a distance equal to the radius, R, from the pointed end. Then rotate the compass around the centre to draw the circle. Alternatively, tack a string to the centre of the circle, tie a pencil a distance R away, and trace the circle with the pencil.

5. 5

Cut out the traced circle.

6. 6

Draw a straight line from the edge to the marked centre with a ruler and pencil.

7. 7

Calculate the size of the pie wedge to cut out of the circle using the following formula: D = 360*√[1-(H/R)^2], where D is the number of degrees of the portion of the circle you want to make into your cone. In other words, D is 360 times the square root of 1 minus H/R squared.

8. 8

Place the eye of the protractor at the centre of the circle. Place the protractor's baseline over the line you just drew on the circle. Find D degrees on the protractor. Put a mark next to the angle.

Note: Protractors go up to only 180 degrees. If D is greater than 180, subtract D from 360 and find that angle on the protractor instead.

9. 9

Draw a line from the circle's centre through the mark you just made, and extend the line with a straightedge or ruler to the edge of the circle.

10. 10

Cut along the two straight lines that meet at the circle centre to cut out a triangular pie wedge. If the angle D you found in step 7 is less than 180 degrees, you'll use the wedge to make your cone. If D is greater than 180, then you'll use the larger part of the circle.

11. 11

Join the two edges of the appropriate part of the circle to make your cone.

12. 12

Paste or tape some extra paper or cloth material on the underside of the two edges you just joined to hold the cone together.

#### Tips and warnings

• Note that you can make two cones with the same dimensions by cutting a circle in half. (See the Resources link below.) In fact, both the wedge and the part of the circle remaining after the wedge is removed can be made into cones. The smaller portion will result in a taller and narrower cone, the larger portion will be shorter and wider.

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