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First of all you should draw your cone in elevation and plan as shown in Figure 1. Divide your plan view up into equal segments. I have broken the plan view shown up into twelve (12) equal segments. (The accuracy of the development will increase with the number of segments that you break the plan view of the cone into.) For twelve (12) equal divisions break the plan view up by drawing lines through the centre line at 30, 60 90 and 180 degrees. We will use these divisions in a couple of steps but first we must lay out the initial overall cone development. An finally draw lines from every arc back to the center of the main development as shown in Figure 8. We can disregard the top half of the main development as the equal divisions form your full cone development.

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Note: If this cone was to be cut out of steel these lines from the circumference to the center are actually called press lines. You can check your work by printing out the development. Cut around the outline of the development and lightly folding each press line down.

Join the two outside straight edges with sticky tape and there you have your cone! Finally I promised a mathematical formula to help produce a more accurate cone development. The inaccuracy occurs when you use a compass to break your cone base circle up into equal segments. You can check this buy measuring one of your arc lengths and multiplying this by the number of divisions. Compare this result with the formula for the circumference of a circle which equals Pi times by diameter.

You will notice the calculated result is longer. Now to help produce your accurate cone development use this formula: Angle = (D1 x 360) / D2 Where: • Angle = the included angle between the outside lines of the main development • D1 = the diameter is of the base of the cone (see diagram below) • D2 = the diameter is of the developed cone, which you get from the elevation of your cone (see diagram below) To use this formula, scribe your main development radius then draw your horizontal line. Then use the formula to calculate the included angle of the outside lines, grab a protractor (or use AutoCAD) and measure/draw this included angle out from the horizontal line. I am having problems physically drawing the development of a cone. It keeps coming up short, like you have mentioned.

I have had a read through this information, and i see that the equation at the bottom keeps coming up with the same answer. It doesn't matter what numbers you put in there. It still comes out with 360. The circumference of a circle is worked out by: pi x diameter = c so the equation ACTUALLY looks like this: ( PI x D ) X 360 angle = ----------------- PI x D so therefore you cancel out the PI x D on the top and bottom and you are left with angle = 360.