Lateral Surface of a ConeDate: 02/10/99 at 21:08:51 From: Grant Subject: Lateral surface of cone What is the equation for the lateral surface of a cone? Date: 02/11/99 at 12:51:55 From: Doctor Peterson Subject: Re: Lateral surface of cone Hi, Grant. Welcome to the Doctor's office. I can take your question two ways: the formula for the lateral surface area, or the equation of the surface itself (involving x, y, and z coordinates). I'll assume it's the former. You can find the formula on this page: http://mathforum.org/dr.math/faq/formulas/faq.cone.html The area is pi*r*s, where r is the radius of the base, and s is the length of the side (from the vertex to the base). You can figure it out without too much trouble if you think of the surface as made of a piece of paper rolled up. Unroll it flat, and it will be a sector of a circle: ********* ****** ****** *** / ** / ** / * / * /s * / * / * / * / * +---------------------* * * * * * * * * * * * * ** ** ** ** *** *** 2 pi r ****** ****** ********* The arc length of the whole circle would be 2 pi s; but you only have as much as will fit around the base of the cone, 2 pi r. That means you have 2 pi r r ------ = --- 2 pi s s of the whole circle, so the area is r --- * pi s^2 = pi * r * s s - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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