



 
Jonathan, I have drawn what I see as your cone sleeve. Do I have the angle correct? I need some additional information. Can you tell me the radius and either the height or the slant height? Penny Jon wrote back
I redrew my diagram and labeled it. I changed the angle measurement from 22^{o} to t^{o} so that what I do applied to other sleeves as well. The circumference of the circle at the base of the cone is 2 π r units. When you slice the cone and roll it out flat you get a sector of a circle of radius s units and a central angle that measures w^{o}. The circle of radius s has a circumference of 2 π s units and the arc of length 2 π r is a portion of that circumference just as w^{o} is a portion of the entire central angle of the circle of 360^{0}. In fact by the symmetry of the circle these proportions are the same. That is or This give you the angle measurement you require from r and s. If you can't measure the radius of the base r or the slant height s directly you can calculate them using the trigonometric relations relating r, s and h.
I hope this helps,  


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