       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>

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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 ?

>