Formula for the Surface of a Cylinder
Date: Tue, 2 Jul 1996 13:47:47 -0400 (EDT) From: Anonymous Subject: General cylinder surface formula Hi, My son studied (amongst other things) cylinders in his math class last semester. The class covered the formula for a right cylinder, but my son is curious to know the general formula for cylinders in any orientation. In other words, given two three-dimensional end points (x0, y0, z0) and (x1, y1, z1), and the radius of the cylinder, what would be the resulting formula to describe the surface of the cylinder? I've looked around a lot on the Internet, but I haven't been able to find the general formula. We figure it must be similar to the sphere formula x*x + y*y + z*z = r*r. Also, we think that the equation will be the equivalent of an infinite number of circles, all perpendicular to and centered around the line from the first point to the second. We'd certainly appreciate any help you can offer. Thanks! Graham MacRobie (for Andrew MacRobie)
Date: Tue, 2 Jul 1996 18:06:43 -0400 (EDT) From: Dr. Anthony Subject: Re: General cylinder surface formula If you slice through a circular cylinder in a direction which is not perpendicular to the axis, then the shape of the figure produced will be an ellipse. If therefore we have a cylinder with its two end planes not at right angles to the axis, then the curved surface area would be the perimeter of the ellipse multiplied by the perpendicular height. Since calculating the perimeter of an ellipse involves a particularly difficult integral, it is certain that there will be no convenient formula for the surface area. The volume, on the other hand would be relatively easy to calculate, using the formula pi*a*b for the cross-section area of the ellipse, where 2a and 2b are the major and minor axes of the ellipse. -Doctor Anthony, The Math Forum
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