Diameter of Cone FrustumDate: 05/24/2000 at 05:39:25 From: Vin Subject: Diameter of cone Dear Dr. Math, I need to solve for the diameter of a cone when it is opened up flat. The inner and outer diameters, and the height are given. The top part of the cone is cut of by the inner diameter. Kindly help me. Date: 05/24/2000 at 09:05:42 From: Doctor Peterson Subject: Re: Diameter of cone Hi, Vin. It's not quite clear whether the inner and outer diameters you are given refer to the bases of the frustum of a cone, or to the flattened shape; I'll assume you mean you are given D, d, and h in this side view of a frustum: d +----+----+ / | \ / | \ / | \ / |h \ / | \ / | \ / | \ +------------+------------+ D You can find the total height of the uncut cone using similar triangles: + ----------------- /|\ | / | \l | / | \ | / | r\ | +----+----+ | L/ | \ H / | \ | / | \ | / |h \ | / | \ | / | \ | / | \ | +------------+------------+ ---- R Then the radii of the circles you get when you flatten the cone are the slant heights L and l of the cone, which you can find using the Pythagorean theorem. Write back if you need more help. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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