Conical SectionsDate: 08/02/99 at 11:00:48 From: Dave Cope Subject: Conical sections If I know the angle and the diameter of one end of a cone and the length of the cone, what is the diameter of the other end of the cone? Date: 08/02/99 at 13:15:38 From: Doctor Peterson Subject: Re: Conical sections Hi, Dave. Since a cone has only one end, I'll assume you're referring to a frustum of a cone, like a cylinder with sloped sides. I'm also not sure what angle you're referring to, so I'll take it to be the angle between the sides and vertical. Also I'll assume you know the actual (perpendicular) height, not the slant height along the side. Then you have this: + /|\ / |A\ / | \ / | \ / | r1 \ +-----+-----+ / | |\ / | |A\ / | | \ / | | \ / | | \ / h| | \ / | | \ / | | \ / | | \ / | | r2-r1 \ +----------------+-----+----------+ r2 Then we have a right triangle with legs h and r2-r1 and angle A; trigonometry gives us r2 - r1 ------- = tan A h so r2 = r1 + h tan A If any of these measurements are not what you have, or if you need help finding the tangent of the angle, let me know. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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