Re: Calculation of the surface after intersection of two spheres

*To*: mathgroup at smc.vnet.net*Subject*: [mg100905] Re: Calculation of the surface after intersection of two spheres*From*: dh <dh at metrohm.com>*Date*: Thu, 18 Jun 2009 04:50:44 -0400 (EDT)*References*: <h19i7g$p78$1@smc.vnet.net>

Hi Horacius, place the spheres symmetrical on the x axis at -0.5 and 0.5. Then the intersection is at x=0. The total surface is twice that of one sphere. Now, consider the truncated sphere as a rotation surface. The radius: y[x] as a function of x. Use the formula for the surface of a rotation body. Then integrate for x=0 to x=1.1. This is implemented her: =========================================== r = 0.6; x0 = 0.5; y[x_] = Sqrt[r^2 - (x - x0)^2]; Plot[ {y[x, 0.5]}, {x, 0, 1.1}, AspectRatio -> Automatic] 2 Integrate[2 y[x] Pi Sqrt[1 + y'[x]^2], {x, 0, 1.1}] ========================================== Daniel Horacius ReX wrote: > Hi, > > I have two spheres of radius 0.6 whose origins are separated a > distance of 1. So the spheres overlap and I want to calculate the > total surface now. > > For that purpose I started to calculate the surface of the separated > spheres, which is trivial and I can do by hand, but after they > intersect or overlap, how can I tell the program to calculate the > surface ? > > Thanks in advance >