- ZosoAchilles
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- Noble Member
Hylebos and Coxx, I believe we're all right. My answer is slightly different because I defined the angle (theta) from the surface of the table to the outside of the cone, whereas is seems you two defined it to the inside of the cone (thus my angle = 180 - your angle.)
For the hell of it, here is my process:
1.The arc length of the edge of the circle from the removed wedge is r*a
2. The maximum circumference of the cone is therefore 2*pi*r-r*a, or rewritten as 2*pi(r-(r*a)/(2*pi)), where I can define R = (r-(r*a)/(2*pi)).
3. From trigonometry, cos(180-theta) = R/r, which reduces to cos(theta) = -R/r. Remember I defined theta as the angle from the table to the outside of the cone.
4. Therefore, theta = arccos(-R/r), or theta = arccos(a/(2*pi)-1)
EDIT: Yeah, I need to type faster. Congrats :)
[Edited on 07.13.2012 1:15 PM PDT]