Surface Area of Cones and PyramidsDate: 09/27/2003 at 21:41:33 From: Nadiya Subject: Surface area of cones and pyramids Can the method for finding the surface area of a pyramid be used as well to find the surface area of a cone? Date: 09/28/2003 at 10:40:46 From: Doctor Jerry Subject: Re: Surface area of cones and pyramids Hi Nadiya, Yes, if you're willing to be a bit loose with procedures. The area of pyramid is 2*a*s, where a is the side of the base and s the slant height. I suppose one can find this by looking at one triangle, whose area is (1/2) * height * base = (1/2)*s*(a) There are four of these, for a total area of 2*a*s. On the cone, divide the circle into a large number of equal pieces, say n of them. We know that each has a base of length 2*pi*r/n. So, this is a. The slant height is s. Each base can be connected to the vertex, making a "triangle." The resulting area is (1/2) * s * 2*pi*r/n There are n of these for a total area of pi*r*s. I believe that Kepler used these kinds of (risky) arguments. - Doctor Jerry, The Math Forum http://mathforum.org/dr.math/ |
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